
M. Tiersch, G. G. Guerreschi, J. Clausen, H. J. Briegel Approaches to Measuring Entanglement in Chemical Magnetometers,
J. Phys. Chem. A. 118 13, (20131210),
URL doi:10.1021/jp408569d (ID: 718583)
Toggle Abstract
Chemical magnetometers are radical pair systems such as solutions of pyrene and N,Ndimethylaniline (Py–DMA) that show magnetic field effects in their spin dynamics and their fluorescence. We investigate the existence and decay of quantum entanglement in free geminate Py–DMA radical pairs and discuss how entanglement can be assessed in these systems. We provide an entanglement witness and propose possible observables for experimentally estimating entanglement in radical pair systems with isotropic hyperfine couplings. As an application, we analyze how the field dependence of the entanglement lifetime in Py–DMA could in principle be used for magnetometry and illustrate the propagation of measurement errors in this approach.

B. P. Lanyon, P. Jurcevic, M. Zwerger, C. Hempel, E. A. Martínez, W. Dür, H. J. Briegel, R. Blatt, C. F. Roos Measurementbased quantum computation with trapped ions,
Phys. Rev. Lett. 111 210501, (20131119),
URL DOI: 10.1103/PhysRevLett.111.210501 (ID: 718582)
Toggle Abstract
Measurementbased quantum computation represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the oneway quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of measurementbased quantum computation using deterministically generated cluster states, in a system of trapped calcium ions. First we implement a universal set of operations for quantum computing. Second we demonstrate a family of measurementbased quantum error correction codes and show their improved performance as the code length is increased. The methods presented can be directly scaled up to generate graph states of several tens of qubits.

H. J. Briegel, S. Popescu Intramolecular refrigeration in enzymes,
Proc. R. Soc. A 469 20110290, (20130731),
URL doi: 10.1098/rspa.2011.0290 (ID: 646657)
Toggle Abstract
We present a simple mechanism for intramolecular
refrigeration, where parts of a molecule are actively
cooled below the environmental temperature. We
discuss the potential role and applications of such
a mechanism in biology, in particular in enzymatic
reactions.

M. Zwerger, H. J. Briegel, W. Dür Universal and Optimal Error Thresholds for MeasurementBased Entanglement Purification,
Phys. Rev. Lett. 110 260503, (20130628),
URL DOI: 10.1103/PhysRevLett.110.260503 (ID: 718479)
Toggle Abstract
We investigate measurementbased entanglement purification protocols (EPP) in the presence of local noise and imperfections. We derive a universal, protocolindependent threshold for the required quality of the local resource states, where we show that local noise per particle of up to 24% is tolerable. This corresponds to an increase of the noise threshold by almost an order of magnitude, based on the joint measurementbased implementation of sequential rounds of fewparticle EPP. We generalize our results to multipartite EPP, where we encounter similarly high error thresholds.

G. G. Guerreschi, M. Tiersch, U. Steiner, H. J. Briegel Optical switching of radical pair conformation enhances magnetic sensitivity,
Chem. Phys. Lett. 572 106, (20130530),
URL doi:10.1016/j.cplett.2013.04.010 (ID: 718346)
Toggle Abstract
The yield of radical pair reactions is influenced by magnetic fields well beyond the levels expected from energy considerations. This dependence can be traced back to the microscopic dynamics of electron spins and constitutes the basis of chemical compasses. Here we propose a new experimental approach based on molecular photoswitches to achieve additional control on the chemical reaction and allow shorttime resolution of the spin dynamics. Our proposal enables experiments to test some of the standard assumptions of the radical pair model and improves the sensitivity of a paradigmatic model of chemical magnetometer by up to two orders of magnitude.

A. Asadian, D. Manzano, M. Tiersch, H. J. Briegel Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions,
Phys. Rev. E 87 012109, (20130110),
URL 10.1103/PhysRevE.87.012109 (ID: 718076)
Toggle Abstract
In ddimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperatures, which are coupled to opposite ends of the lattice, with a focus on the validity of Fourier's law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the nonequilibrium steady state using the rotatingwave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.

J. Clausen, G. G. Guerreschi, M. Tiersch, H. J. Briegel Multiple reencounter approach to radical pair reactions and the role of nonlinear master equations,
(20131023),
URL (ID: 718622)
Toggle Abstract
We formulate a multipleencounter model of the radical pair mechanism that is based on a random coupling of the radical pair to a minimal model environment. These occasional pulselike couplings correspond to the radical encounters and give rise to both dephasing and recombination. While this is in agreement with the original model of Haberkorn and its extensions that assume additional dephasing, we show how a nonlinear master equation may be constructed to describe the conditional evolution of the radical pairs prior to the detection of their recombination. We propose a nonlinear master equation for the evolution of an ensemble of independently evolving radical pairs whose nonlinearity depends on the record of the fluorescence signal. We also reformulate Haberkorn's original argument on the physicality of reaction operators using the terminology of quantum optics/open quantum systems. Our model allows one to describe multiple encounters within the exponential model and connects this with the master equation approach. We include hitherto neglected effects of the encounters, such as a separate dephasing in the triplet subspace, and predict potential new effects, such as Grover reflections of radical spins, that may be observed if the strength and time of the encounters can be experimentally controlled.

A. Makmal, M. Zhu, D. Manzano, M. Tiersch, H. J. Briegel Quantum walks on embedded hypercubes,
(20130920),
URL (ID: 718625)
Toggle Abstract
It has been proved by Kempe that discrete quantum walks on the hypercube (HC) hit exponentially faster than the classical analog. The same was also observed numerically by Krovi and Brun for a slightly different property, namely, the expected hitting time. Yet, to what extent this striking result survives in more general graphs, is to date an open question. Here we tackle this question by studying the expected hitting time for quantum walks on HCs that are embedded into larger symmetric structures. By performing numerical simulations of the discrete quantum walk and deriving a general expression for the classical hitting time, we observe an exponentially increasing gap between the expected classical and quantum hitting times, not only for walks on the bare HC, but also for a large family of embedded HCs. This suggests that the quantum speedup is stable with respect to such embeddings.

S. Barz, R. Vasconcelos, C. Greganti, M. Zwerger, W. Dür, H. J. Briegel, P. Walther Demonstrating elements of measurementbased quantum error correction,
(20130823),
URL (ID: 718598)
Toggle Abstract
In measurementbased quantum computing an algorithm is performed by measurements on highlyentangled resource states. To date, several implementations were demonstrated, all of them assuming perfect noisefree environments. Here we consider measurementbased information processing in the presence of noise and demonstrate all elements of quantum error correction. We implement the protocol using a fourqubit photonic cluster state, where we first encode a general qubit nonlocally such that phase errors can be detected. We then read out the error syndrome and analyze the output states after decoding. Our demonstration is independent of the physical system and shows an important building block for measurementbased quantum computing which is crucial for realistic scenarios.

M. Zwerger, H. J. Briegel, W. Dür Hybrid architecture for encoded measurementbased quantum computation,
(20130821),
URL (ID: 718584)
Toggle Abstract
We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurementbased approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurementbased way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within this error model we find a threshold of the order of 10% local noise per particle for faulttolerant quantum computation and quantum communication.

J. Mautner, A. Makmal, D. Manzano, M. Tiersch, H. J. Briegel Projective simulation for classical learning agents: a comprehensive investigation,
(20130507),
URL (ID: 718513)
Toggle Abstract
We study the model of projective simulation (PS), a novel approach to artificial intelligence based on the stochastic processing of episodic memory, which was first introduced in [H.J. Briegel and G. De las Cuevas. Sci. Rep. 2, 400, (2012)]. Throughout the paper we provide a detailed analysis of the PS features and examine its performances, where we mainly focus on its achievable efficiency and learning times. We situate the PS agent in different learning scenarios, and study its learning abilities. A variety of scenarios are being considered, thereby demonstrating the model's flexibility. In addition, to put the PS scheme in context, we compare its performance with those of Qlearning and learning classifier systems, two popular representatives of artificial intelligence models. It is shown that PS is a competitive artificial intelligence model of unique properties and strengths.

D. Manzano, M. Tiersch, A. Asadian, H. J. Briegel Quantum transport efficiency and Fourier's law,
Phys. Rev. E 86 061118, (20121213),
URL (ID: 717838)
Toggle Abstract
We analyze the steadystate energy transfer in a chain of coupled twolevel systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. Implications of these results on energy transfer in biological light harvesting systems, and the role of quantum coherences and entanglement are discussed.

M. Tiersch, H. J. Briegel Decoherence in the chemical compass: The role of decoherence for avian magnetoreception,
Phil. Trans. R. Soc. A. 370 4517, (20120928),
URL doi: 10.1098/rsta.2011.0488 (ID: 718181)
Toggle Abstract
Contrary to the usual picture that decoherence destroys quantum properties and causes the quantumtoclassical transition, we argue that decoherence can also play a constructive role in driving quantum dynamics and amplifying its results to macroscopic scales. We support this perspective by presenting an example system from spin chemistry, which is also of importance for biological systems, e.g. in avian magnetoreception.

M. Tiersch, S. Popescu, H. J. Briegel A critical view on transport and entanglement in models of photosynthesis,
Phil. Trans. R. Soc. A. 370 3771, (20120813),
doi: 10.1098/rsta.2011.0202 (ID: 717739)
Toggle Abstract
We revisit critically the recent claims, inspired by quantum optics and quantum information, that there is entanglement in the biological pigment–protein complexes, and that it is responsible for the high transport efficiency. While unexpectedly long coherence times were experimentally demonstrated, the existence of entanglement is, at the moment, a purely theoretical conjecture; it is this conjecture that we analyse. As demonstrated by a toy model, a similar transport phenomenology can be obtained without generating entanglement. Furthermore, we also argue that, even if entanglement does exist, it is purely incidental and seems to play no essential role for the transport efficiency. We emphasize that our paper is not a proof that entanglement does not exist in lightharvesting complexes—this would require a knowledge of the system and its parameters well beyond the state of the art. Rather, we present a counterexample to the recent claims of entanglement, showing that the arguments, as they stand at the moment, are not sufficiently justified and hence cannot be taken as a proof for the existence of entanglement, let alone of its essential role, in the excitation transport.

H. J. Briegel On creative machines and the physical origins of freedom,
Scientific Reports 522, (20120720),
doi:10.1038/srep00522 (ID: 718192)
Toggle Abstract
We discuss the possibility of free behavior in embodied systems that are, with no exception and at all scales of their body, subject to physical law. We relate the discussion to a model of an artificial agent that exhibits a primitive notion of creativity and freedom in dealing with its environment, which is part of a recently introduced scheme of information processing called projective simulation. This provides an explicit proposal on how we can reconcile our understanding of universal physical law with the idea that higher biological entities can acquire a notion of freedom that allows them to increasingly detach themselves from a strict dependence on the surrounding world.

M. Zwerger, W. Dür, H. J. Briegel Measurementbased quantum repeaters,
Phys. Rev. A 85 062326, (20120627),
DOI: 10.1103/PhysRevA.85.062326 (ID: 718250)

G. G. Guerreschi, J. Cai, S. Popescu, H. J. Briegel Persistent dynamic entanglement from classical motion: how biomolecular machines can generate nontrivial quantum states,
New J. Phys. 14 053043, (20120529),
DOI: 10.1088/13672630/14/5/053043 (ID: 718251)

H. J. Briegel, G. De las Cuevas Projective simulation for artificial intelligence,
Scientific Reports 2 400, (20120515),
DOI:10.1038/srep00400 (2012) (ID: 718249)
Toggle Abstract
We propose a model of a learning agent whose interaction with the environment is governed by a simulationbased projection, which allows the agent to project itself into future situations before it takes real action. Projective simulation is based on a random walk through a network of clips, which are elementary patches of episodic memory. The network of clips changes dynamically, both due to new perceptual input and due to certain compositional principles of the simulation process. During simulation, the clips are screened for specific features which trigger factual action of the agent. The scheme is different from other, computational, notions of simulation, and it provides a new element in an embodied cognitive science approach to intelligent action and learning. Our model provides a natural route for generalization to quantummechanical operation and connects the fields of reinforcement learning and quantum computation.

M. Tiersch, U. Steiner, S. Popescu, H. J. Briegel Open Quantum System Approach to the Modeling of Spin Recombination Reactions,
J. Phys. Chem. A. 116 4020, (20120308),
(ID: 718075)
Toggle Abstract
In theories of spindependent radical pair reactions, the time evolution of the radical pair, including the effect of the chemical kinetics, is described by a master equation in the Liouville formalism. For the description of the chemical kinetics, a number of possible reaction operators have been formulated in the literature. In this work, we present a framework that allows for a unified description of the various proposed mechanisms and the forms of reaction operators for the spinselective recombination processes. On the basis of the concept that master equations can be derived from a microscopic description of the spin system interacting with external degrees of freedom, it is possible to gain insight into the underlying microscopic processes and develop a systematic approach toward determining the specific form of the reaction operator in concrete scenarios.

J. Cai, S. Popescu, H. J. Briegel Dynamic entanglement in oscillating molecules and potential biological implications,
Phys. Rev. E 82 021921, (20100825),
URL DOI: 10.1103/PhysRevE.82.021921 (ID: 616945)
Toggle Abstract
We demonstrate that entanglement can persistently recur in an oscillating twospin molecule that is coupled to a hot and noisy environment, in which no static entanglement can survive. The system represents a nonequilibrium quantum system which, driven through the oscillatory motion, is prevented from reaching its (separable) thermal equilibrium state. Environmental noise, together with the driven motion, plays a constructive role by periodically resetting the system, even though it will destroy entanglement as usual. As a building block, the present simple mechanism supports the perspective that entanglement can exist also in systems which are exposed to a hot environment and to high levels of decoherence, which we expect, e.g., for biological systems. Our results also suggest that entanglement plays a role in the heat exchange between molecular machines and environment. Experimental simulation of our model with trapped ions is within reach of the current stateoftheart quantum technologies.

A. Asadian, M. Tiersch, G. G. Guerreschi, J. Cai, S. Popescu, H. J. Briegel Motional effects on the efficiency of excitation transfer,
12 075019, (20100726),
URL doi: 10.1088/13672630/12/7/075019 (ID: 717104)
Toggle Abstract
Energy transfer plays a vital role in many natural and technological processes. In this work, we study the effects of mechanical motion on the excitation transfer through a chain of interacting molecules with applications to biological scenarios of transfer processes. Our investigation demonstrates that, for various types of mechanical oscillations, the transfer efficiency is significantly enhanced over that of comparable static configurations. This enhancement is a genuine quantum signature and requires the collaborative interplay between the quantumcoherent evolution of the excitation and the mechanical motion of the molecules; it has no analogue in the classical incoherent energy transfer. This effect may not only occur naturally but also be exploited in artificially designed systems to optimize transport processes. As an application, we discuss a simple and hence robust control technique.

J. Cai, G. G. Guerreschi, H. J. Briegel Quantum control and entanglement in a chemical compass,
Phys. Rev. Lett. 104 220502, (20100604),
URL doi:10.1103/PhysRevLett.104.220502 (ID: 686698)
Toggle Abstract
The radicalpair mechanism is one of the two main hypotheses to explain the navigability of animals in weak magnetic fields, enabling, e.g., birds to see Earth’s magnetic field. It also plays an essential role in spin chemistry. Here, we show how quantum control can be used to either enhance or reduce the performance of such a chemical compass, providing a new route to further study the radicalpair mechanism and its applications. We study the role of radicalpair entanglement in this mechanism, and demonstrate its intriguing connections with the magneticfield sensitivity of the compass. Beyond their immediate application to the radicalpair mechanism, these results also demonstrate how stateoftheart quantum technologies could potentially be used to probe and control biological functions.

J. Cai, A. Miyake, W. Dür, H. J. Briegel Universal quantum computer from a quantum magnet,
Phys. Rev. A 82 052309, (20100413),
URL DOI: 10.1103/PhysRevA.82.052309 (ID: 717195)
Toggle Abstract
We show that a local Hamiltonian of spin3/2 particles with only twobody nearestneighbor AffleckKennedyLiebTasaki and exchangetype interactions has a unique ground state, which can be used to implement universal quantum computation merely with singlespin measurements. We prove that the Hamiltonian is gapped, independent of the system size. Our result provides a further step toward utilizing systems with condensedmattertype interactions for measurementbased quantum computation.

G. De las Cuevas, W. Dür, H. J. Briegel, M. A. MartinDelgado Mapping all classical spin models to a lattice gauge theory,
12 043014, (20100408),
URL doi:10.1088/13672630/12/4/043014 (ID: 716799)
Toggle Abstract
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be expressed as a special instance of the partition function of a 4dimensional pure LGT with gauge group Z_2 (4D Z_2 LGT). This provides a unification of models with apparently very different features into a single complete model. The result uses an equality between the Hamilton function of any classical spin model and the Hamilton function of a model with all possible kbody Isingtype interactions, for all k, which we also prove. Here, we elaborate on the proof of the result, and we illustrate it by computing quantities of a specific model as a function of the partition function of the 4D Z_2 LGT. The result also allows one to establish a new method to compute the meanfield theory of Z_2 LGTs with d > 3, and to show that computing the partition function of the 4D Z_2 LGT is computationally hard (#P hard). The proof uses techniques from quantum information.

C. Mora, M. Piani, A. Miyake, M. van den Nest, W. Dür, H. J. Briegel Universal resources for approximate and stochastic measurementbased quantum computation,
Phys. Rev. A 81 042315, (20100400),
URL DOI: 10.1103/PhysRevA.81.042315 (ID: 693347)
Toggle Abstract
We investigate which quantum states can serve as universal resources for approximate and stochastic measurementbased quantum computation in the sense that any quantum state can be generated from a given resource by means of singlequbit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting, for example, from a restriction to finite measurement settings or from possible imperfections in the resources or local operations. We show that entanglementbased criteria for universality obtained in M. Van den Nest et al. [New J. Phys. 9, 204 (2007)] for the exact, deterministic case can be lifted to the much more general approximate, stochastic case. This allows us to move from the idealized situation (exact, deterministic universality) considered in previous works to the practically relevant context of nonperfect state preparation. We find that any entanglement measure fulfilling some basic requirements needs to reach its maximum value on some element of an approximate, stochastic universal family of resource states, as the resource size grows. This allows us to rule out various families of states as being approximate, stochastic universal. We prove that approximate, stochastic universality is in general a weaker requirement than deterministic, exact universality and provide resources that are efficient approximate universal, but not exact deterministic universal. We also study the robustness of universal resources for measurementbased quantum computation under realistic assumptions about the (imperfect) generation and manipulation of entangled states, giving an explicit expression for the impact that errors made in the preparation of the resource have on the possibility to use it for universal approximate and stochastic state preparation. Finally, we discuss the relation between our entanglementbased criteria and recent results regarding the uselessness of states with a high degree of geometric entanglement as universal resources [D. Gross et al., Phys. Rev. Lett. 102, 190501 (2009); M. J. Bremner et al., Phys. Rev. Lett 102, 190502 (2009)].

O. Gittsovich, R. Hübener, E. Rico Ortega, H. J. Briegel Local renormalization method for random systems,
025020, (20100302),
URL oai:arXiv.org:0908.1312 (ID: 716784)
Toggle Abstract
In this paper, we introduce a realspace renormalization transformation for random spin systems on 2D lattices. The general method is formulated for random systems and results from merging two well known real space renormalization techniques, namely the strong disorder renormalization technique (SDRT) and the contractor renormalization (CORE). We analyze the performance of the method on the 2D random transverse field Ising model (RTFIM).

M. van den Nest, W. Dür, R. Raussendorf, H. J. Briegel Quantum algorithms for spin models and simulable gate sets for quantum computation,
Phys. Rev. A 80 052334, (20091130),
URL DOI: 10.1103/PhysRevA.80.052334 (ID: 595921)
Toggle Abstract
We present simple mappings between classical lattice models and quantum circuits, which provide a systematic formalism to obtain quantum algorithms to approximate partition functions of lattice models in certain complexparameter regimes. We, e.g., present an efficient quantum algorithm for the sixvertex model as well as a twodimensional Isingtype model. We show that classically simulating these (complexparameter) spin models is as hard as simulating universal quantum computation, i.e., BQP complete (BQP denotes boundederror quantum polynomial time). Furthermore, our mappings provide a framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. We, e.g., show that the simulability of Valiant's match gates can be recovered by using the solvability of the freefermion eightvertex model.

R. Hübener, M. van den Nest, W. Dür, H. J. Briegel Classical spin systems and the quantum stabilizer formalism: general mappings and applications,
Proc. R. Soc. A 50 083303, (20090827),
URL oai:arXiv.org:0812.2127 (ID: 644261)
Toggle Abstract
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum stabilizer states and product states, thereby generalizing mappings for some specific models established in [Phys. Rev. Lett. 98, 117207 (2007)]. For Ising and Pottstype models with and without external magnetic field, we show how the entanglement features of the corresponding stabilizer states are related to the interaction pattern of the classical model, while the choice of product states encodes the details of interaction. These mappings establish a link between the fields of classical statistical mechanics and quantum information theory, which we utilize to transfer techniques and methods developed in one field to gain insight into the other. For example, we use quantum information techniques to recover well known duality relations and local symmetries of classical models in a simple way, and provide new classical simulation methods to simulate certain types of classical spin models. We show that in this way all inhomogeneous models of qdimensional spins with pairwise interaction pattern specified by a graph of bounded treewidth can be simulated efficiently. Finally, we show relations between classical spin models and measurementbased quantum computation.

E. Rico Ortega, R. Hübener, S. Montangero, N. Moran, B. Pirvu, J. Vala, H. J. Briegel Valence Bond States: Link models,
Annals of Physics 324 1875, (20090807),
URL oai:arXiv.org:0811.1049 (ID: 651264)
Toggle Abstract
An isotropic antiferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and to the nonlinear sigma model) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known antiferromagnetic MottHubbard insulators is given by means of the twopoint equaltime correlation function obtained i) numerically from the suggested state and ii) experimentally from neutron scattering on cuprates in the antiferromagnetic insulator phase.

H. J. Briegel, D. Browne, W. Dür, R. Raussendorf, M. van den Nest Measurementbased quantum computation,
Nature Physics 5 19, (20090100),
URL doi:10.1038/nphys1157 (ID: 646711)
Toggle Abstract
Quantum computation offers a promising new kind of information processing, where the nonclassical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation exist. These models have been shown to be formally equivalent, but their underlying elementary concepts and the requirements for their practical realization can differ significantly. A particularly exciting paradigm is that of measurementbased quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state. We review recent developments in measurementbased quantum computation with a view to both fundamental and practical issues, in particular the power of quantum computation, the protection against noise (fault tolerance) and steps towards experimental realization. Finally, we highlight a number of connections between this field and other branches of physics and mathematics.

G. Toth, C. Knapp, O. Gühne, H. J. Briegel Spin squeezing and entanglement,
Phys. Rev. A 79 042334, (2009),
URL doi:10.1103/PhysRevA.79.042334 (ID: 596901)
Toggle Abstract
What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components J_k. They can be used for the experimental detection of entanglement in a system of spin1/2 particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of: (i) the mean values and variances of J_k in three orthogonal directions, or (ii) the variances of J_k in three orthogonal directions, or (iii) the mean values of J_k^2 in three orthogonal directions or (iv) the mean values and variances of J_k in arbitrary directions. We compare our inequalities to known spin squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced twoqubit states. Finally, we apply our criteria for entanglement detection in spin models, showing that they can be used to detect bound entanglement in these systems.

G. De las Cuevas, W. Dür, M. van den Nest, H. J. Briegel Completeness of classical spin models and universal quantum computation,
J. Stat. Mech. P07001, (2009),
URL doi: 10.1088/17425468/2009/07/P07001 (ID: 644262)
Toggle Abstract
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence of an inhomogeneous magnetic field, can specialize to the partition function of any Ising system on an arbitrary graph. In this sense the 2D Ising model is said to be "complete". However, in order to obtain the above result, the coupling strengths on the 2D lattice must assume complex values, and thus do not allow for a physical interpretation. Here we show how a complete model with real and, hence, "physical" couplings can be obtained if the 3D Ising model is considered. We furthermore show how to map general qstate systems with possibly manybody interactions to the 2D Ising model with complex parameters, and give completeness results for these models with real parameters. We also demonstrate that the computational overhead in these constructions is in all relevant cases polynomial. These results are proved by invoking a recently found crossconnection between statistical mechanics and quantum information theory, where partition functions are expressed as quantum mechanical amplitudes. Within this framework, there exists a natural correspondence between manybody quantum states that allow universal quantum computation via local measurements only, and complete classical spin systems.

G. De las Cuevas, W. Dür, H. J. Briegel, M. A. MartinDelgado Unifying all classical spin models in a Lattice Gauge Theory,
Phys. Rev. Lett. 102 230502, (2009),
URL doi: 10.1103/PhysRevLett.102.230502 (ID: 644263)
Toggle Abstract
We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z_2 LGT. In this way, all classical spin models with apparently very different features are unified in a single complete model, and a physical relation between all models is established. As applications of this result, we present a new method to do mean field theory for abelian discrete LGTs with d>3, and we show that the computation of the partition function of the 4D Z_2 LGT is a computationally hard (#Phard) problem. We also extend our results to abelian continuous models, where we show the approximate completeness of the 4D Z_2 LGT. All results are proven using quantum information techniques.

J. Cai, W. Dür, M. van den Nest, A. Miyake, H. J. Briegel Quantum computation in correlation space and extremal entanglement,
Phys. Rev. Lett. 103 050503, (2009),
URL doi:10.1103/PhysRevLett.103.050503 (ID: 657743)
Toggle Abstract
Recently, a framework was established to systematically construct novel universal resource states for measurementbased quantum computation using techniques involving finitely correlated states. With these methods, universal states were found which are in certain ways much less entangled than the original cluster state model, and it was hence believed that with this approach many of the extremal entanglement features of the cluster states could be relaxed. The new resources were constructed as "computationally universal" statesi.e. they allow one to efficiently reproduce the classical output of each quantum computationwhereas the cluster states are universal in a stronger sense since they are "universal state preparators". Here we show that the new resources are universal state preparators after all, and must therefore exhibit a whole class of extremal entanglement features, similar to the cluster states.

A. Asadian, J. Cai, G. G. Guerreschi, H. J. Briegel Motional effects on the efficiency of excitation transfer in photosynthetic complexes,
2nd Black Forest Focus on Soft Matter, "Quantum Efficiency: from Biology to Material Science" (Titisee, Black Forest, Germany, 20091022), (20091022),
(ID: 716800)

T. Carle, W. Dür, H. J. Briegel, B. Kraus Spin gases and manybody phase gates,
Joint Annual Meeting of ÖPG/SPS/ÖGAA (Innsbruck, Austria, 20090902), URL (20090902),
(ID: 717286)
Toggle Abstract
Spin gases are a natural extension of a classical gas, particles move along a classical trajectory, but carry a quantum degree of freedom, which can interact during collisions. The interaction of two particles is modelled with 2body phase gates and therefore the overall quantum state is a weighted graph state (WGS). We generalize this description to morebody interactions
in oder to study the decoherence process between a system and a bath as well as time evolution and entanglement properties of the system. The states we using are the so called LME states (LME  Locally Maximally Entanglable), those states are generated by nbody phase gates corresponding to nbody interactions. It is shown how nbody phase gates can be decomposed
into 2body phase gates, how the reduced density matrix for a state generated by 3body phase gates can be calculated explicitly and how it can be extended to morebody interactions. Furthermore we analyze the decoherence process under manybody phase gate interactions between the system and bath. We derive decoherence maps for an arbitrary number of system qubits interacting
with an bath of qubits (spin bath) via general nbody phase gate interactions. We can treat Markovian as well as NonMarkovian scenarios.

T. Carle, W. Dür, H. J. Briegel, B. Kraus Spin gases and manybody phase gates,
SCALA Summer School (Cargèse, France, 20090817), URL (20090817),
(ID: 717285)
Toggle Abstract
Spin gases are a natural extension of a classical gas, particles move along a classical trajectory, but carry a quantum degree of freedom, which can interact during collisions. The interaction of two particles is modelled with 2body phase gates and therefore the overall quantum state is a weighted graph state (WGS). We generalize this description to morebody interactions
in oder to study the decoherence process between a system and a bath as well as time evolution and entanglement properties of the system. The states we using are the so called LME states (LME  Locally Maximally Entanglable), those states are generated by nbody phase gates corresponding to nbody interactions. It is shown how nbody phase gates can be decomposed
into 2body phase gates, how the reduced density matrix for a state generated by 3body phase gates can be calculated explicitly and how it can be extended to morebody interactions. Furthermore we analyze the decoherence process under manybody phase gate interactions between the system and bath. We derive decoherence maps for an arbitrary number of system qubits interacting
with an bath of qubits (spin bath) via general nbody phase gate interactions. We can treat Markovian as well as NonMarkovian scenarios.

T. Carle, C. Kruszynska, W. Dür, H. J. Briegel, B. Kraus Classes of multipartite entangled states and applications,
SFB meeting Vienna (Vienna, Austria), (20090424),
(ID: 717284)
Toggle Abstract
One of the challenges in quantum information theory is to get a better understanding of multipartite entangled states their entanglement properties and their applications. Despite all the results on bipartite entanglement, the properties of multipartite entangled states are far from being completely understood. In order to gain new insight, a new class of multipartite entangled states was recently introduced [C. Kruszynska, B. Kraus, Phys. Rev. A, 79, 052304 (2009)]. It is based on the physical idea of how well the qubits can be locally entangled to an auxillary system (LME  Locally Maximally Entanglable). Prominent examples of this class are stabilizer states, which are used for quantum error correction and oneway computing, and weighted graph states. The aim here is to consider a restricted set of LMEs to generalise the existing description of spin gases using weighted graph states.

G. De las Cuevas, W. Dür, H. J. Briegel, M. A. MartinDelgado Unifying all classical spin models in a lattice gauge theory,
SCALA Conference 2009 (Cortina d'Ampezzo, Italy, 20090215), (20090200),
(ID: 658043)

G. De las Cuevas, W. Dür, H. J. Briegel, M. MartinDelgado Unifying all classical spin models in a lattice gauge theory,
SFB Conference (Innsbruck, Austria, 20090129), (20090100),
(ID: 658041)

J. Cai, G. G. Guerreschi, S. Popescu, H. J. Briegel Dynamic Entanglement in Oscillating Molecules and Potential Biological Implications,
SFB Conference (Innsbruck, Austria, 20090129), (2009),
(ID: 657741)

J. Cai, G. G. Guerreschi, S. Popescu, H. J. Briegel Dynamic Entanglement in Oscillating Molecules and Potential Biological Implications,
SCALA Conference 2009 (Cortina d'Ampezzo, Italy, 20090215), (2009),
(ID: 687004)

A. Asadian, J. Cai, G. G. Guerreschi, H. J. Briegel Motional effects on the efficiency of excitation transfer in photosynthetic complexes,
Workshop on Quantum Effects in Biological Systems, QuEBS 2009 (Lisbon, Portugal, 20090707), (2009),
(ID: 693959)

G. G. Guerreschi, J. Cai, S. Popescu, H. J. Briegel Quantum entanglement and offequilibrium thermodynamics of oscillating molecules,
Workshop on Quantum Effects in Biological Systems, QuEBS 2009 (Lisbon, Portugal, 20090707), (2009),
(ID: 693960)

J. Cai, W. Dür, M. van den Nest, A. Miyake, H. J. Briegel Quantum computation in correlation space and extremal entanglement,
International Conference on Quantum Foundation and Technology: Frontier and Future (ICQFT'09) (Shanghai, China, 20090717), URL (2009),
(ID: 697383)

E. Rico Ortega, H. J. Briegel 2D multipartite valence bond states in quantum antiferromagnets,
Annals of Physics 323 2115, (20080420),
DOI: 10.1016/j.aop.2008.03.006 (ID: 718252)

M. van den Nest, H. J. Briegel Measurementbased quantum computation on graph states and undecidable logic theories,
Foundations of Physics 38 448, (2008),
URL oai:arXiv.org:quantph/0610040 (ID: 428204)
Toggle Abstract
We establish a connection between measurementbased computation on graph states and the field of mathematical logic. We show that the computational power of graph states as resources for measurementbased quantum computation is reflected in the expressive power of (classical) formal logic languages defined on the underlying graphs. In particular, it is shown that for all graph states which disallow efficient classical simulation of measurementbased quantum computations, the underlying graphs are associated with undecidable logic theories. Here undecidability is to be interpreted in the sense of Goedel, meaning that there exist propositions, expressible in the above classical formal logic, which cannot be proven or disproven.

M. van den Nest, K. Luttmer, W. Dür, H. J. Briegel Graph states as ground states of manybody spin1/2 Hamiltonians,
Phys. Rev. A 77 012301, (2008),
URL doi:10.1103/PhysRevA.77.012301 (ID: 432907)
Toggle Abstract
We consider the problem whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most twobody interactions, we show that no nqubit graph state can be the exact, nondegenerate ground state. We determine for any graph state the minimal d such that it is the nondegenerate ground state of a dbody interaction Hamiltonian, while we show for d'body Hamiltonians H with d'n spins.

W. Dür, M. Bremner, H. J. Briegel Quantum simulation of interacting highdimensional systems: the influence of noise,
Phys. Rev. A 78 052325, (2008),
URL DOI:10.1103/PhysRevA.78.052325 (ID: 489122)
Toggle Abstract
We consider the simulation of interacting highdimensional systems using pairwise interacting qubits. The main tool in this context is the generation of effective manybody interactions, and we examine a number of different protocols for obtaining them. These methods include the usage of higherorder processes (commutator method), unitary conjugation or graph state encoding, as well as teleportation based approaches. We illustrate and compare these methods in detail and analyze the time cost for simulation. In the second part of the article, we investigate the influence of noise on the simulation process. We concentrate on errors in the interaction Hamiltonians and consider two generic noise models, (i) timing errors in pairwise interactions and (ii) noisy pairwise interactions described by Master equations of Lindblad form. We analyze and compare the effect of noise for the different simulation methods and propose a way to significantly reduce the influence of noise by making use of entanglement purification together with a teleportation based protocol.

M. van den Nest, W. Dür, H. J. Briegel Completeness of the classical 2D Ising model and universal quantum computation,
Phys. Rev. Lett. 100 110501, (2008),
URL DOI:10.1103/PhysRevLett.100.110501 (ID: 513147)
Toggle Abstract
We prove that the 2D Ising model is \emph{complete} in the sense that the
partition function of any classical $q$state spin
model (on an arbitrary graph) can be expressed as a special instance of the
partition function of a 2D Ising model with complex inhomogeneous
couplings and external fields. In the case where the
original model is an Ising or Pottstype
model, we find that the corresponding 2D square lattice
requires only polynomially more spins w.r.t the original
one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are
established by connecting classical spin models with
measurementbased quantum computation and invoking the
universality of the 2D cluster states.

C. Mora, M. Piani, H. J. Briegel Epsilon measures of entanglement,
10 083027, (2008),
URL doi: 10.1088/13672630/10/8/083027 (ID: 613149)
Toggle Abstract
We associate to every entanglement measure a family of measures which depend on a precision parameter, and which we call εmeasures of entanglement. Their definition aims at addressing a realistic scenario in which we need to estimate the amount of entanglement in a state that is only partially known. We show that many properties of the original measure are inherited by the family, in particular weak monotonicity under transformations applied by means of local operations and classical communication (LOCC). On the other hand, they may increase on average under stochastic LOCC. Remarkably, the εversion of a convex entanglement measure is continuous even if the original entanglement measure is not, so that the εversion of an entanglement measure may be actually considered a smoothed version of it.

S. Anders, H. J. Briegel, W. Dür A variational method based on weighted graph states,
9 361, (20070600),
URL doi:10.1088/13672630/9/10/361 (ID: 489124)
Toggle Abstract
In a recent article [Phys. Rev. Lett. *97* (2006), 107206], we have presented
a class of states which is very suitable as a variational set to find ground
states in spin systems of arbitrary spatial dimension and with longrange
entanglement. Here, we continue the exposition of our technique, extend from
spin 1/2 to higher spins and use the boson Hubbard model as a nontrivial
example to demonstrate our scheme. We also demonstrate the extraction of
nonlocal groundstate properties from the approximation.
(local copy)

W. Dür, H. J. Briegel Entanglement purification and quantum error correction,
Rep. Prog. Phys. 70 1381, (20070500),
URL doi:10.1088/00344885/70/8/R03 (ID: 461087)
Toggle Abstract
We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on the theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, which highlights the fact that entanglement purification is a fundamental tool in quantum information processing.
(local copy)

M. van den Nest, W. Dür, H. J. Briegel Classical spin models and the quantum stabilizer formalism,
Phys. Rev. Lett. 98 117207, (20070300),
URL doi:10.1103/PhysRevLett.98.117207 (ID: 418259)
Toggle Abstract
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of qstate spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum information theory, such as the stabilizer formalism and classical simulation techniques, to gain general insights into these models in a unified way. We recover and generalize several symmetries and highlow temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded treewidth.
(local copy)

J. Calsamiglia, L. Hartmann, W. Dür, H. J. Briegel Entanglement and decoherence in spin gases,
International Journal of Quantum Information 5 509523, (2007),
URL doi:10.1142/S0219749907003018 (ID: 314175)
Toggle Abstract
We study the dynamics of entanglement in spin gases. A spin gas consists of a
(large) number of interacting particles whose random motion is described
classically while their internal degrees of freedom are described
quantummechanically. We determine the entanglement that occurs naturally in
such systems for specific types of quantum interactions. At the same time,
these systems provide microscopic models for nonMarkovian decoherence: the
interaction of a group of particles with other particles belonging to a
background gas are treated exactly, and differences between collective and
noncollective decoherence processes are studied. We give quantitative results
for the Boltzmann gas and also for a lattice gas, which could be realized by
neutral atoms hopping in an optical lattice. These models can be simulated
efficiently for systems of mesoscopic sizes (N ~ 10^5).
(local copy)

M. van den Nest, W. Dür, G. Vidal, H. J. Briegel Classical simulation versus universality in measurement based quantum computation,
Phys. Rev. A 75 012337, (2007),
URL doi:10.1103/PhysRevA.75.012337 (ID: 388976)
Toggle Abstract
We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidtrank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidtrank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement based quantum computation is possible for all states with logarithmically bounded Schmidtrank width (with respect to the system size). For graph states where the Schmidtrank width scales in this way, we efficiently construct the optimal tree tensor network descriptions, and provide several examples. We highlight parallels in the efficient description of complex systems in quantum information theory and graph theory.
(local copy)

L. Hartmann, B. Kraus, H. J. Briegel, W. Dür On the role of memory errors in quantum repeaters,
Physical Review A (Atomic, Molecular, and Optical Physics) 75 032310, (2007),
URL doi:10.1103/PhysRevA.75.032310 (ID: 398614)
Toggle Abstract
We investigate the influence of memory errors in the quantum repeater scheme for longrange quantum communication. We show that the communication distance is limited in standard operation mode due to memory errors resulting from unavoidable waiting times for classical signals. We show how to overcome these limitations by (i) improving local memory and (ii) introducing two operational modes of the quantum repeater. In both operational modes, the repeater is run blindly, i.e., without waiting for classical signals to arrive. In the first scheme, entanglement purification protocols based on oneway classical communication are used allowing to communicate over arbitrary distances. However, the error thresholds for noise in local control operations are very stringent. The second scheme makes use of entanglement purification protocols with twoway classical communication and inherits the favorable error thresholds of the repeater run in standard mode. One can increase the possible communication distance by an order of magnitude with reasonable overhead in physical resources. We outline the architecture of a quantum repeater that can possibly ensure intercontinental quantum communication.
(local copy)

L. Hartmann, J. Calsamiglia, W. Dür, H. J. Briegel Weighted graph states and applications to spin chains, lattices and gases,
J. Phys. B: At. Mol. Opt. Phys. 40 S1S44, (2007),
doi:10.1088/09534075/40/9/S01 (ID: 423727)
Toggle Abstract
Weighted graph states naturally arise when spin systems interact via an Isingtype interaction. First, we abstractly define the class of weighted graph states and demonstrate its computational accessibility. We show how reduced density matrices of a small number of spins (about 10) can be computed from arbitrarily large systems using weighted graph techniques and projected entangled pairs techniques, and we discuss various entanglement measures accessible from these reduced density matrices. Second, we apply these findings to spin chains and lattices with longrange interactions and analytically derive area laws for the scaling of blockwise entanglement. Then, we turn to disordered spin systems, spin gases, which are connected to random weighted graph states and which share their entanglement properties. Finally, we use a spin gas as a bath that introduces decoherence in single as well as multipartite spin systems.
The microscopic, exact decoherence model we obtain can operate in different regimes and exhibit nonMarkovian features as well as spatially correlated noise effects.
(local copy)

C. Mora, H. J. Briegel, B. Kraus Quantum Kolmogorov complexity and its applications,
International Journal of Quantum Information 5 729, (2007),
URL 10.1142/S0219749907003171 (ID: 424322)
Toggle Abstract
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure nqubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

M. van den Nest, W. Dür, A. Miyake, H. J. Briegel Fundamentals of universality in oneway quantum computation,
9 204, (2007),
URL doi:10.1088/13672630/9/6/204 (ID: 445781)
Toggle Abstract
In this article, we build a framework allowing for a
systematic investigation of the fundamental issue:
\emph{``Which quantum states serve as universal resources
for measurementbased (oneway) quantum computation?''} We
start our study by reexamining what is exactly meant by
``universality'' in quantum computation, and what the
implications are for universal oneway quantum computation.
Given the framework of a measurementbased quantum
computer, where quantum information is processed by
\emph{local} operations only, we find that the most general
universal oneway quantum computer is one which is capable
of accepting arbitrary classical inputs and producing
arbitrary quantum outputswe refer to this property as
\emph{CQuniversality}. We then show that a systematic
study of CQuniversality in oneway quantum computation is
possible by identifying entanglement features that are
required to be present in every universal resource. In
particular, we find that a large class of entanglement
measures must reach its supremum on every universal
resource. These insights are used to identify several
families of states as being not universal, such as 1D
cluster states, GHZ states, W states, and ground states of
noncritical 1D spin systems. Our criteria are strengthened
by considering the efficiency of a quantum computation, and
we find that entanglement measures must obey a certain
scaling law with the system size for all efficient
universal resources. This again leads to examples of
nonuniversal resources, such as, e.g., ground states of
critical 1D spin systems. On the other hand, we provide
several examples of efficient universal resources, namely
graph states corresponding to hexagonal, triangular and
Kagome lattices. Finally, we consider the more general
notion of encoded CQuniversality, where quantum outputs
are allowed to be produced in an encoded form. Again we
provide entanglementbased criteria for encoded
universality. Moreover, we present a general procedure to
construct encoded universal resources.
(local copy)

T. Konrad, O. Gühne, J. Audretsch, H. J. Briegel Parameter estimation for mixed states from a single copy,
Phys. Rev. A 75 062101, (2007),
URL doi:10.1103/PhysRevA.75.062101 (ID: 448346)
Toggle Abstract
Given a single copy of a mixed state of the form \rho=\lambda\rho_1+(1\lambda)\rho_2, what is the optimal measurement to estimate the parameter \lambda, if \rho_1 and \rho_2 are known? We present a general strategy to obtain the optimal measurements employing a Bayesian estimator. The measurements are chosen to minimize the deviation between the estimated and the true value of \lambda. We explicitly determine the optimal measurements for a general twodimensional system and for important higher dimensional cases.
(local copy)

G. Toth, C. Knapp, O. Gühne, H. J. Briegel Optimal spin squeezing inequalities detect bound entanglement in spin models,
Phys. Rev. Lett. 99 250405, (2007),
URL doi:10.1103/PhysRevLett.99.250405 (ID: 448347)
Toggle Abstract
We determine the complete set of generalized spin squeezing inequalities. These are entanglement criteria that can be used for the experimental detection of entanglement in a system of spin(1/2) particles in which the spins cannot be individually addressed. They can also be used to show the presence of bound entanglement in the thermal states of several spin models.
(local copy)

L. Hartmann, W. Dür, H. J. Briegel Entanglement and its dynamics in open, dissipative systems,
New J. Phys. 9 230, (2007),
doi:10.1088/13672630/9/7/230 (ID: 502750)
Toggle Abstract
Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gastype systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states. We develop master equations to describe the system and its interaction with an environment, study toy models with two particles (qubits), where the master equation can often be solved analytically, and finally examine larger systems with possibly fluctuating particle numbers. We find that in gastype systems, the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment, while this is not true in strongly coupled systems. But even then the temperature range where one can find entangled steady states is typically much higher with the reset mechanism.
(local copy)

H. J. Briegel Entanglement in spin gases & lattices; weighted graph states,
Interfaces between Physics and Computer Science, Summer School (Bremen, 20070611), URL (20070622),
(ID: 511589)

H. J. Briegel Theory of measurementbased quantum computation  Cluster and graph states as entanglement resources criteria for universality,
Interfaces between Physics and Computer Science, Summer School (Bremen, 20070611), URL (20070622),
(ID: 511590)

H. J. Briegel Universality and simulation of measurementbased quantum computation,
QAA07: 2007 Workshop in Quantum Algorithms and Applications, Sydney (Sydney, Australia, 20070528), URL (20070529),
(ID: 505219)

H. J. Briegel Universality and classical simulation of quantum computation,
GRC on Quantum Information Science (Il Ciocco, Barga, Italy, 20070415), URL (20070416),
(ID: 505223)

H. J. Briegel Universality and classical simulation of quantum computation,
71. Jahrestagung der Deutschen Physikalischen Gesellschaft und DPG Frühjahrstagung des Arbeitskreises Festkörperphysik (Regensburg, Germany, 20070326), URL (20070329),
(ID: 505631)
Toggle Abstract
We will review recent work on the theoretical foundations of quantum
computation and the role of entanglement in this context [1,2].
In the measurementbased (oneway) model of quantum computation
[3], the resource character of entanglement is particularly highlighted.
We have recently found necessary criteria that relate the entanglement
of the resource state to its universality and/or to the classical
simulatability of the measurementbased computation. These investigations
shed some new light on the basic questions ”What are the
essential features that give quantum computers their additional power
over classical devices?” and ”Which types of quantum algorithms can
be simulated efficiently by a classical Turing machine”.

H. J. Briegel Universal resources for measurementbased quantum computation,
International Workshop on Measurementbased quantum computing (MBQC) (Oxford, 20070318), URL (20070318),
(ID: 461784)
Toggle Abstract
What are the essential features that give quantum computers their additional power over classical devices? We study this question within the framework of measurementbased (oneway) quantum computation, where it can be posed in a much more concise form, amenable to quantitative analysis. In the present talk, we will first reconsider the notion of universality for quantum computation and, more specifically, for oneway quantum computation. We will then present necessary criteria, in terms of entanglement measures, that a resource has to fulfil, in order to qualify as a universal resource in the oneway model. Similar criteria must be fulfilled by the resource if a oneway quantum computer using this resource is to provide a speedup over a classical computer.
Main part of the talk is based on recent work with Maarten van den Nest, Wolfgang Dür, Akimasa Miyake, and Guifre Vidal.

H. J. Briegel Entanglement in quantum systems far away from TD equilibrium Are there nontrivial quantum effects in biology?,
Noise Information & Complexity @ Quantum Scale (Ettore Majorana Centre, Erice (Sicily), Italy, 20071104), URL (2007),
(ID: 539992)
Toggle Abstract
Noise and information, often believed to be opposite notions, have a common denominator: stochastic processes. It is the interest of an observer that turns a stochastic process into a noise source or into an information source. At the hearth of any stochastic process is randomness, which naturally leads to the idea of “many possibilities”. This, in turns, admits varying degrees of complication, hence the notion of complexity.
In recent years these concepts have been applied down to the quantum scale, giving rise to a variety of intriguing phenomena and potential applications.
The aim of this meeting is to bring together scientists working with stochastic processes in quantum domain to put forward recent advancements in the fields of quantum statistical mechanics and quantum information, emphasizing interdisciplinary aspects and methods.
Topics covered:
quantum fluctuations and noise, quantum measurements, quantum error correction, quantum control, quantum entanglement, quantum algorithms, quantum complex structures, quantum networks, quantum communication, quantum entropies, quantum computational complexity, quantum communication complexity, quantum devices, quantum complex dynamics, quantum stochastic resonance, quantum chaos, quantum statistics and thermodynamics.

W. Dür, M. van den Nest, H. J. Briegel Classical spin models and the quantum stabilizer formalism,
Computational Complexity of Quantum Hamiltonian Systems (Lorentz Center, Leiden, NL, 20070723), URL (20070700),
(ID: 510449)
Toggle Abstract
We introduce a connection of a large class of classical statistical mechanical models on arbitrary graphs including Ising and Potts model with magnetic fields as special instances to quantum information theory. We show how to express the partition function ZG of such models as overlaps between stabilizer (or graph) states that encode the interaction pattern and complete product states that specify the interaction strengthes and temperature. We utilize this connection in both directions. For instance, we obtain new classical algorithms to calculate ZG and to establish general symmetry and highlow temperature duality relations. We also show that techniques and results established in classical statistical mechanics (e.g. efficient classical simulation techniques) can be utilized in measurementbased quantum computation (MQC), e.g. to obtain new ways of classically simulating MQC on certain resource states. In addition, we use the relation to establish a strong universality result for the 2DIsing model, namely that the partition function of any other such model on an arbitrary interaction graph can be expressed as a special instance of the partition function of the 2D Ising model on a (polynomially) enlarged lattice.

M. van den Nest, W. Dür, G. Vidal, H. J. Briegel Classical simulation of measurementbased quantum computation,
MBQC 2007 (Oxford, United Kingdom, 20070319), (20070319),
(ID: 504049)
Toggle Abstract
We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidtrank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidtrank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement based quantum computation is possible for all states with logarithmically bounded Schmidtrank width (with respect to the system size). For graph states where the Schmidtrank width scales in this way, we efficiently construct the optimal tree tensor network descriptions, and provide several examples. We highlight parallels in the efficient description of complex systems in quantum information theory and graph theory.

O. Gittsovich, H. J. Briegel Covariance matrices and the separability problem,
QUROPE Winter School 2007 (Obergurgl, Austria, 20070000), (2007),
(ID: 504055)
Toggle Abstract
We present a unifying approach to the separability problem for
finite dimensional systems. Our method uses a representation of a
quantum state by a covariance matrix of suitable observables. On the one
hand, our approach leads to entanglement criteria that detect all
entangled states of two qubits, as well as indeed many bound entangled
states and, on the other hand, provides a framework to link and
understand several existing criteria like crossnorm (or realignment)
criterion, a recent criterion using Bloch representation or the local
uncertainty relations.}

R. Hübener, S. Anders, C. Kruszynska, L. Hartmann, F. Verstraete, W. Dür, H. J. Briegel Efficient Numerical Simulations of Quantum systems,
International Conference on Quantum Information Processing and Communication (Barcelona, Spain, 20070000), (2007),
(ID: 553364)
Toggle Abstract
Recently, a number of novel techniques have been proposed for numerical
treatment of spin systems, specifically aiming at the study of ground state
properties and time evolution. We have introduced a variational method
based on socalled weighted graph states, a class of states with intrinsic
longrange entanglement and suitability for arbitrary geometries. Here we
present new results, specifically on the application of our method for bosonic
systems such as BoseHubbard model and also compare it with other methods.
Further, we have investigated possibilities to form a hybrid technique using the
weighted graph states and projected entangled pair states or tensor tree
networks.

C. Kruszynska, A. Miyake, H. J. Briegel, W. Dür Entanglement purification protocols for all graph states,
Physical Review A (Atomic, Molecular, and Optical Physics) 74 052316, (20060600),
URL 10.1103/PhysRevA.74.052316 (ID: 370798)
Toggle Abstract
We present multiparty entanglement purification protocols that are capable of purifying arbitrary graph states directly. We develop recurrence and breeding protocols and compare our methods with strategies based on bipartite entanglement purification in static and communication scenarios. We find that direct multiparty purification is of advantage with respect to achievable yields and minimal required fidelity in static scenarios, and with respect to obtainable fidelity in the case of noisy operations in both scenarios.

M. van den Nest, A. Miyake, W. Dür, H. J. Briegel Universal resources for measurementbased quantum computation,
Phys. Rev. Lett. 97 150504, (20060404),
URL 10.1103/PhysRevLett.97.150504 (ID: 351571)
Toggle Abstract
We investigate which entanglement resources allow universal measurementbased quantum computation via singlequbit operations. We find that any entanglement feature exhibited by the 2D cluster state must also be present in any other universal resource. We obtain a powerful criterion to assess universality of graph states, by introducing an entanglement measure which necessarily grows unboundedly with the system size for all universal resource states. Furthermore, we prove that graph states associated with 2D lattices such as the hexagonal and triangular lattice are universal, and obtain the first example of a universal nongraph state.

A. Trenkwalder, U. Andersen, V. Ahufinger, H. J. Briegel, A. Sanpera, M. Lewenstein Quantum Information Processing in Disordered and Complex Quantum Systems,
Phys. Rev. A 74 062309, (2006),
URL doi:10.1103/PhysRevA.74.062309 (ID: 314184)
Toggle Abstract
We study quantum information processing in complex disordered many body systems that can be implemented by using lattices of ultracold atomic gases and trapped ions. We demonstrate, first in the short range case, the generation of entanglement and the local realization of quantum gates in a disordered magnetic model describing a quantum spin glass. We show that in this case it is possible to achieve fidelities of quantum gates higher than in the classical case. Complex systems with long range interactions, such as ions chains or dipolar atomic gases, can be used to model neural network Hamiltonians. For such systems, where both long range interactions and disorder appear, it is possible to generate long range bipartite entanglement. We provide an efficient analytical method to calculate the time evolution of a given initial state, which in turn allows us to calculate its quantum correlations.
(local copy)

C. Mora, H. J. Briegel Algorithmic complexity of quantum states,
International Journal of Quantum Information 4 715, (2006),
URL doi:10.1142/S0219749906002043 (ID: 314627)
Toggle Abstract
We give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory, the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the string itself. We define the complexity of a quantum state by means of the classical description complexity of an (abstract) experimental procedure that allows us to prepare the state with a given fidelity. We argue that our definition satisfies the intuitive idea of complexity as a measure of "how difficult" it is to prepare a state. We apply this definition to give an upper bound on the algorithmic complexity of a number of known states. Furthermore, we establish a connection between the entanglement of a quantum state and its algorithmic complexity.
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C. Kruszynska, S. Anders, W. Dür, H. J. Briegel Quantum communication cost of preparing multipartite entanglement,
Phys. Rev. A 73 062328, (2006),
URL oai:arXiv.org:quantph/0512218 (ID: 326195)
Toggle Abstract
We study the preparation and distribution of highfidelity multiparty
entangled states via noisy channels and operations. In the particular case of
GHZ and cluster states, we study different strategies using bipartite or
multipartite purification protocols. The most efficient strategy depends on the
target fidelity one wishes to achieve and on the quality of transmission
channel and local operations. We show the existence of a crossing point beyond
which the strategy making use of the purification of the state as a whole is
more efficient than a strategy in which pairs are purified before they are
connected to the final state. We also study the efficiency of intermediate
strategies, including sequences of purification and connection. We show that a
multipartite strategy is to be used if one wishes to achieve high fidelity,
whereas a bipartite strategy gives a better yield for low target fidelity.
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L. Hartmann, W. Dür, H. J. Briegel Steady state entanglement in open and noisy quantum systems at high temperature,
Physical Review A (Atomic, Molecular, and Optical Physics) 74 052304, (2006),
URL doi:10.1103/PhysRevA.74.052304 (ID: 326209)
Toggle Abstract
We show that quantum mechanical entanglement can prevail even in noisy open
quantum systems at high temperature and far from thermodynamical equilibrium,
despite the deteriorating effect of decoherence. The system consists of a
number N of interacting quantum particles, and it can interact and exchange
particles with some environment. The effect of decoherence is counteracted by a
simple mechanism, where system particles are randomly reset to some standard
initial state, e.g. by replacing them with particles from the environment. We
present a master equation that describes this process, which we can solve
analytically for small N. If we vary the interaction strength and the reset
against decoherence rate, we find a threshold below which the equilibrium state
is classically correlated, and above which there is a parameter region with
genuine entanglement.
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S. Anders, H. J. Briegel Fast simulation of stabilizer circuits using a graphstate representation,
Physical Review A 73 022334, (2006),
doi:10.1103/PhysRevA.73.022334 (ID: 340379)
Toggle Abstract
According to the GottesmanKnill theorem, a class of quantum circuits—namely, the socalled stabilizer circuits—can be simulated efficiently on a classical computer. We introduce an algorithm for this task, which is based on the graphstate formalism. It shows significant improvement in comparison to an existing algorithm, given by Gottesman and Aaronson, in terms of speed and of the number of qubits the simulator can handle. We also present an implementation.
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G. Toth, O. Gühne, H. J. Briegel Twosetting Bell inequalities for graph states,
Physical Review A (Atomic, Molecular, and Optical Physics) 73 022303, (2006),
doi:10.1103/PhysRevA.73.022303 (ID: 341123)
Toggle Abstract
We present Bell inequalities for graph states with a high violation of local realism. In particular, we show that there is a basic Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of 2. This inequality needs the measurement of, at most, two operators for each qubit and involves only some of the qubits. We also show that for some families of graph states composite Bell inequalities can be constructed such that the violation of local realism increases exponentially with the number of qubits. We prove that some of our inequalities are facets of the convex polytope containing the manybody correlations consistent with local hidden variable models. Our Bell inequalities are built from stabilizing operators of graph states.
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A. Kay, J. K. Pachos, W. Dür, H. J. Briegel Optimal purification of thermal graph states,
New J. Phys. 8 147, (2006),
URL doi:10.1088/13672630/8/8/147 (ID: 370797)
Toggle Abstract
In this paper, a purification protocol is presented and its performance is proven to be optimal when applied to a particular subset of graph states that are subject to local Znoise. Such mixed states are produced when systems described by graph Hamiltonians are brought into thermal equilibrium. From the optimal protocol, one can derive the exact value of the critical temperature that corresponds to this Hamiltonian, as well as the the related optimal purification rates. A possible implementation of graph Hamiltonians is proposed, which requires only bipartite interactions and local magnetic fields, enabling the tuning of the critical temperature.
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S. Anders, M. Plenio, W. Dür, F. Verstraete, H. J. Briegel GroundState Approximation for Strongly Interacting Spin Systems in Arbitrary Spatial Dimension,
Phys. Rev. Lett. 97 107206, (2006),
doi:10.1103/PhysRevLett.97.107206 (ID: 388950)
Toggle Abstract
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These states allow for the efficient computation of all local observables (e.g., energy) and include states with diverging correlation length and unbounded multiparticle entanglement. As a demonstration, we apply our approach to the Ising model on 1D, 2D, and 3D square lattices. We also present generalizations to higher spins and continuousvariable systems, which allows for the investigation of lattice field theories
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W. Dür, H. J. Briegel Protokolle für die Quanteninformation,
Physik Journal 12 22, (2006),
URL (ID: 420186)
(local copy)

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. J. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Louwenhofen, S. Kröll, G. Leuchs, M. Quantum information processing and communication,
Eur. Phys. J. D 36/2 203  228, (20051101),
URL doi:10.1140/epjd/e2005002511 (ID: 375863)
Toggle Abstract
We present an excerpt of the document “Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe”, which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, http://www.cordis.lu/ist/fet/qipcsr.htm). This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the stateoftheart, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC subfields, that we report here. Dedicated to the memory of Prof. Th. Beth, one of the pioneers of QIPC, whose contributions have had a significant scientific impact on the development as well as on the visibility of a field that he enthusiastically helped to shape since its early days.

J. Calsamiglia, L. Hartmann, W. Dür, H. J. Briegel Spin Gases. Quantum Entanglement Driven by Classical Kinematics,
Phys. Rev. Lett. 95 180502, (2005),
URL doi:10.1103/PhysRevLett.95.180502 (ID: 314174)
Toggle Abstract
A spin gas is a natural extension of a classical gas. It consists of a large number of particles whose (random) motion is described classically, but, in addition, have internal (quantum mechanical) degrees of freedom that interact during collisions. For specific types of quantum interactions we determine the entanglement that occurs naturally in such systems. We analyze how the evolution of the quantum state is determined by the underlying classical kinematics of the gas. For the Boltzmann gas, we calculate the rate at which entanglement is produced and characterize the entanglement properties of the equilibrium state.
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C. Mora, H. J. Briegel Algorithmic Complexity and Entanglement of Quantum States,
Phys. Rev. Lett. 95 200503, (2005),
URL doi:10.1103/PhysRevLett.95.200503 (ID: 314179)
Toggle Abstract
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity.
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A. Miyake, H. J. Briegel Distillation of Multipartite Entanglement by Complementary Stabilizer Measurements,
Phys. Rev. Lett. 95 220501, (2005),
URL doi:10.1103/PhysRevLett.95.220501 (ID: 314180)
Toggle Abstract
We propose a scheme of multipartite entanglement distillation driven by a complementary pair of stabilizer measurements to distill directly a wider range of states beyond the stabilizer code states (such as the GreenbergerHorneZeilinger states). We make our idea explicit by constructing a recurrence protocol for the 3qubit W state (001+010+100). Noisy W states resulting from typical decoherence can be directly purified in a few steps, if their initial fidelity is larger than a threshold. For general input mixed states, we observe distillations to hierarchical fixed points, i.e., not only to the W state but also to the 2qubit Bell pair, depending on their initial entanglement.
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L. Hartmann, J. Calsamiglia, W. Dür, H. J. Briegel Spin gases as microscopic models for nonMarkovian decoherence,
Physical Review A (Atomic, Molecular, and Optical Physics) 72 052107, (2005),
URL doi:10.1103/PhysRevA.72.052107 (ID: 314181)
Toggle Abstract
We analyze a microscopic decoherence model in which the total system is described as a spin gas. A spin gas consists of N classically moving particles with additional, interacting quantum degrees of freedom (e.g., spins). For various multipartite entangled probe states, we analyze the decoherence induced by interactions between the probe and environmental spins in such spin gases. We can treat mesoscopic environments (10^5 particles). We present results for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice, and show the effects of nonMarkovian and correlated noise, as well as finitesize effects.
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O. Gühne, G. Toth, H. J. Briegel Multipartite entanglement in spin chains,
New J. Phys. 7 229, (2005),
URL doi:10.1088/13672630/7/1/229 (ID: 314198)
Toggle Abstract
We investigate the presence of multipartite entanglement in macroscopic spin chains. We discuss the Heisenberg and the XY model and derive bounds on the internal energy for systems without multipartite entanglement. Based on this we show that in thermal equilibrium the abovementioned spin systems contain genuine multipartite entanglement, even at finite modest temperatures.
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W. Dür, L. Hartmann, M. Hein, M. Lewenstein, H. J. Briegel Entanglement in Spin Chains and Lattices with LongRange IsingType Interactions,
Phys. Rev. Lett. 94 097203, (2005),
URL doi:10.1103/PhysRevLett.94.097203 (ID: 314546)
Toggle Abstract
We consider N initially disentangled spins, embedded in a ring or ddimensional lattice of arbitrary geometry, which interact via some longrange Isingtype interaction. We investigate relations between entanglement properties of the resulting states and the distance dependence of the interaction in the limit N. We provide a sufficient condition when bipartite entanglement between blocks of L neighboring spins and the remaining system saturates and determine S_L analytically for special configurations. We find an unbounded increase of S_L as well as diverging correlation and entanglement length under certain circumstances. For arbitrarily large N, we can efficiently calculate all quantities associated with reduced density operators of up to ten particles.
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H. Aschauer, W. Dür, H. J. Briegel Multiparticle entanglement purification for twocolorable graph states,
Physical Review A (Atomic, Molecular, and Optical Physics) 71 012319, (2005),
URL doi:10.1103/PhysRevA.71.012319 (ID: 314548)
Toggle Abstract
We investigate multiparticle entanglement purification schemes which allow one to purify all two colorable graph states, a class of states which includes, e.g., cluster states, GreenbergerHorneZeilinger states, and code words of various error correction codes. The schemes include both recurrence protocols and hashing protocols. We analyze these schemes under realistic conditions and observe for a generic error model that the threshold value for imperfect local operations depends on the structure of the corresponding interaction graph, but is otherwise independent of the number of parties. The qualitative behavior can be understood from an analytically solvable model which deals only with a restricted class of errors. We compare direct multiparticle entanglement purification protocols with schemes based on bipartite entanglement purification and show that the direct multiparticle entanglement purification is more efficient and the achievable fidelity of the purified states is larger. We also show that the purification protocol allows one to produce private entanglement, an important aspect when using the produced entangled states for secure applications. Finally we discuss an experimental realization of a multiparty purification protocol in optical lattices which is issued to improve the fidelity of cluster states created in such systems.
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M. Hein, W. Dür, H. J. Briegel Entanglement properties of multipartite entangled states under the influence of decoherence,
Physical Review A (Atomic, Molecular, and Optical Physics) 71 032350, (2005),
URL doi:10.1103/PhysRevA.71.032350 (ID: 314618)
Toggle Abstract
We investigate entanglement properties of multipartite states under the influence of decoherence. We show that the lifetime of (distillable) entanglement for GreenbergerHorneZeilinger (GHZ)type superposition states decreases with the size of the system, while for a class of other states,namely all graph states with constant degree, the lifetime is independent of the system size. We show that these results are largely independent of the specific decoherence model and are in particular valid for all models which deal with individual couplings of particles to independent environments, described by some quantum optical master equation of Lindblad form. For GHZ states, we derive analytic expressions for the lifetime of distillable entanglement and determine when the state becomes fully separable. For all graph states, we derive lower and upper bounds on the lifetime of entanglement. The lower bound is based on a specific distillation protocol, while upper bounds are obtained by showing that states resulting from decoherence in general become nondistillable or even separable after a finite time. This is done using different methods, namely, (i) the map describing the decoherence process (e.g., the action of a thermal bath on the system) becomes entanglement breaking, (ii) the resulting state becomes separable, and (iii) the partial transposition with respect to certain partitions becomes positive. To this aim, we establish a method to calculate the spectrum of the partial transposition for all mixed states which are diagonal in a graphstate basis. We also consider entanglement between different groups of particles and determine the corresponding lifetimes as well as the change of the kind of entanglement with time. This enables us to investigate the behavior of entanglement under rescaling and in the limit of large number of particles N. Finally we investigate the lifetime of encoded quantum superposition states and show that one can define an effective time in the en
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O. Gühne, G. Toth, P. Hyllus, H. J. Briegel Bell Inequalities for Graph States,
Phys. Rev. Lett. 95 120405, (2005),
URL doi:10.1103/PhysRevLett.95.120405 (ID: 314624)
Toggle Abstract
We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.
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W. Dür, J. Calsamiglia, H. J. Briegel Multipartite secure state distribution,
Physical Review A (Atomic, Molecular, and Optical Physics) 71 042336, (2005),
URL doi:10.1103/PhysRevA.71.042336 (ID: 314625)
Toggle Abstract
We introduce the distribution of a secret multipartite entangled state in a realworld scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations), any state chosen from the set of twocolorable graph states (CalderbankShorSteane codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standard channel purification and teleportation. The parties are thus provided with a secret resource of their choice for distributed secure applications.
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W. Dür, M. Hein, J. I. Cirac, H. J. Briegel Standard forms of noisy quantum operations via depolarization,
Phys. Rev. A 72 052326, (2005),
URL 10.1103/PhysRevA.72.052326 (ID: 340486)
Toggle Abstract
We consider noisy, nonlocal unitary operations or interactions, i.e. the
corresponding evolutions are described by completely positive maps or master
equations of Lindblad form. We show that by random local operations the
completely positive maps can be depolarized to a standard form with a reduced
number of parameters describing the noise process in such a way that the
noiseless (unitary) part of the evolution is not altered. A further reduction
of the parameters, in many cases even to a single one (i.e. global white
noise), is possible by tailoring the decoherence process and increasing the
amount of noise. We generalize these results to the dynamical case where the
ideal unitary operation is given by some interaction Hamiltonian. The resulting
standard forms may be used to compute lower bounds on channel capacities, to
simplify quantum process tomography or to derive error thresholds for
entanglement purification and quantum computation.

C. Mora, H. J. Briegel Algorithmic complexity of quantum states,
International Summer School on Quantum Information “ISSQUI 05” (Dresden, Germany, 20050926), (20050926),
(ID: 351432)
Toggle Abstract
We give a definition for the Kolmogorov complexity of a pure quantum
state. In classical information theory the algorithmic complexity of a
string is a measure of the information needed by a universal machine
to reproduce the string itself. We define the complexity of a quantum
state by means of the classical description complexity of an
(abstract) experimental procedure that allows us to prepare the state
with a given fidelity. We argue that our definition satisfies the
intuitive idea of complexity as a measure of ``how difficult'' it is
to prepare a quantum state. We apply this definition to give an upper
bound for the algorithmic complexity of a number of states. We also
investigate the relation between the algorithmic complexity of a
quantum state and its entanglement properties.

C. Mora, H. J. Briegel Algorithmic complexity of quantum states,
International School of Physics "Enrico Fermi" (Varenna, Italy, 20050705), (20050705),
(ID: 351433)
Toggle Abstract
We give a definition for the Kolmogorov complexity of a pure quantum
state. In classical information theory the algorithmic complexity of a
string is a measure of the information needed by a universal machine
to reproduce the string itself. We define the complexity of a quantum
state by means of the classical description complexity of an
(abstract) experimental procedure that allows us to prepare the state
with a given fidelity. We argue that our definition satisfies the
intuitive idea of complexity as a measure of ``how difficult'' it is
to prepare a quantum state. We apply this definition to give an upper
bound for the algorithmic complexity of a number of states. We also
investigate the relation between the algorithmic complexity of a
quantum state and its entanglement properties.

A. Miyake, H. J. Briegel Multipartite entanglement distillation for the W state,
International School of Physics ``Enrico Fermi'', ``Quantum computers, algorithms and chaos'' (Varenna, Italy, 20050705), (20050705),
(ID: 351617)
Toggle Abstract
We propose a scheme of multipartite entanglement distillation driven by a complementary pair of stabilizer measurements, to distill directly a wider range of states beyond the stabilizer code states (such as the GreenbergerHorneZeilinger states). We make our idea explicit by constructing a recurrence protocol for the 3qubit W state. Noisy W states resulting from typical decoherence can be directly purified in a few steps, if their initial fidelity is larger than a threshold. For general input mixed states, we observe distillations to hierarchical fixed points, i.e., not only to the W state but also to the 2qubit Bell pair, depending on their initial entanglement.

C. Mora, H. J. Briegel Algorithmic complexity of quantum states,
Quantum Optics Obergurgl Meeting (Obergurgl, Austria, 20050227), (20050227),
(ID: 351434)
Toggle Abstract
We give a definition for the Kolmogorov complexity of a pure quantum
state. In classical information theory the algorithmic complexity of a
string is a measure of the information needed by a universal machine
to reproduce the string itself. We define the complexity of a quantum
state by means of the classical description complexity of an
(abstract) experimental procedure that allows us to prepare the state
with a given fidelity. We argue that our definition satisfies the
intuitive idea of complexity as a measure of ``how difficult'' it is
to prepare a quantum state. We apply this definition to give an upper
bound for the algorithmic complexity of a number of states. We also
investigate the relation between the algorithmic complexity of a
quantum state and its entanglement properties.

A. Miyake, H. J. Briegel Wstate entanglement purification protocols,
Obergurgl meeting 2005 Quantum Optics (Obergurgl, Austria, 20050227), (20050227),
(ID: 351616)
Toggle Abstract
We present entanglement purification protocols for W states. This state is not included in the socalled graph states, which implies the stabilizers are not necessarily the product of the Pauli operators. It has interesting properties such as good fault tolerance for local noise and qubit loss. Our protocol can be said to be the first entanglement purification protocol for the nongraph states. This enlarges the application range of entanglement purification protocols, which would be useful in stabilizing the wider range of quantum states. Also, as a simple case, we show that the threshold fidelity of distillability for the Wernerlike input is about 0.58.

M. Hein, W. Dür, J. I. Cirac, H. J. Briegel Standard forms of noisy evolutions via depolarization,
Quantum Optics Meeting (Obergurgl, Austria, 20050227), (20050200),
(ID: 352047)

J. Calsamiglia, L. Hartmann, W. Dür, H. J. Briegel Spin gases: classical kinematics drives quantum entanglement,
Quantum Optics Meeting (Obergurgl, Austria, 20050227), (20050200),
(ID: 352050)

L. Hartmann, J. Calsamiglia, W. Dür, H. J. Briegel Spin gases: classical thermodynamics drives the quantum state,
Obergurgl Meeting 2005 (20050000), (2005),
(ID: 332864)
Toggle Abstract
We study the dynamics of entanglement in spin gases. A spin gas consists of a large number of interacting particles whose (random) motion is described classically, and internal (quantum mechanical) degrees of freedom are taken into account. For specific types of quantum interactions we determine the natural entanglement that occurs in such systems. We analyze how the evolution of the quantum states is determined by the underlying classical thermodynamics of the gas. For the Boltzmann gas, we compute the rate at which entanglement is produced at short times and characterize the entanglement properties of the equilibrium state. We also present numerical results for a lattice gas, which could be realized by neutral atoms hopping in an optical lattice. Our methods also allow us to study (collective and noncollective) decoherence processes within a microscopic model for nonMarkovian decoherence. We can efficiently simulate systems of mesoscopic sizes (N=10^5)

O. Gühne, G. Toth, P. Hyllus, H. J. Briegel Bell inequalities for graph states,
Obergurgl Meeting 2005 (20050000), (2005),
(ID: 334439)
Toggle Abstract
We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits.

C. Kruszynska, S. Anders, W. Dür, H. J. Briegel Quantum Communication Cost of Preparing Multipartite Entanglement,
Obergurgl Meeting 2005 (20050000), (2005),
(ID: 340481)
Toggle Abstract
We study the preparation and distribution of highfidelity multiparty entangled states. There are several possibilities to do that, and which is most efficient depends on the target fidelity one whishes to achieve and on the quality of transmission channel and local operations at one's disposal. We show how to choose the optimal strategy for a variety of settings.

C. Kruszynska, S. Anders, W. Dür, H. J. Briegel Quantum Communication Cost of Preparing Multipartite Entanglement,
Abschlusskolloquium
DFGSchwerpunktprogramm, QuantenInformationsverabeitung (Bad Honneff, Germany, 20050000), (2005),
(ID: 352335)
Toggle Abstract
We study the preparation and distribution of highfidelity multiparty entangled states. There are several possibilities to do that, and which is most efficient depends on the target fidelity one whishes to achieve and on the quality of transmission channel and local operations at one's disposal. We show how to choose the optimal strategy for a variety of settings.

C. Kruszynska, S. Anders, W. Dür, H. J. Briegel Quantum Communication Cost of Preparing Multipartite Entanglement,
International School of Physics Enrico Fermi on Quantum Computers,
Algorithms and Chaos (Varenna, Italy, 20050000), (2005),
(ID: 352336)
Toggle Abstract
We study the preparation and distribution of highfidelity multiparty entangled states. There are several possibilities to do that, and which is most efficient depends on the target fidelity one whishes to achieve and on the quality of transmission channel and local operations at one's disposal. We show how to choose the optimal strategy for a variety of settings.

Z. Zhao, Y. Chen, A. N. Zhang, T. Yang, H. J. Briegel, J. Pan Experimental demonstration of fivephoton entanglement and opendestination teleportation,
Nature 430 54, (2004),
URL doi: 10.1038/nature02643 (ID: 314354)
Toggle Abstract
Quantummechanical entanglement of three or four particles has been achieved experimentally, and has been used to demonstrate the extreme contradiction between quantum mechanics and local realism. However, the realization of fiveparticle entanglement remains an experimental challenge. The ability to manipulate the entanglement of five or more particles is required for universal quantum error correction. Another key process in distributed quantum information processing, similar to encoding and decoding, is a teleportation protocol that we term opendestination teleportation. An unknown quantum state of a single particle is teleported onto a superposition of N particles; at a later stage, this teleported state can be read out (for further applications) at any of the N particles, by a projection measurement on the remaining particles. Here we report a proofofprinciple demonstration of fivephoton entanglement and opendestination teleportation (for N=3). In the experiment, we use two entangled photon pairs to generate a fourphoton entangled state, which is then combined with a singlephoton state. Our experimental methods can be used for investigations of measurementbased quantum computation and multiparty quantum communication.
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H. Aschauer, J. Calsamiglia, M. Hein, H. J. Briegel Local invariants for multipartite entangled states allowing for a simple entanglement criterion,
Quantum Information and Computation (online) 4 383, (2004),
URL oai:arXiv.org:quantph/0306048 (ID: 314385)
Toggle Abstract
We present local invariants of multipartite pure or mixed states, which can be easily calculated and have a straightforward physical meaning. As an application, we derive a new entanglement criterion for arbitrary mixed states of n parties. The new criterion is weaker than the partial transposition criterion but offers advantages for the study of multipartite systems. A straightforward generalization of these invariants allows for the construction of a complete set of observable polynomial invariants.
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W. Dür, H. J. Briegel Stability of Macroscopic Entanglement under Decoherence,
Phys. Rev. Lett. 92 180403, (2004),
URL doi:10.1103/PhysRevLett.92.180403 (ID: 314550)
Toggle Abstract
We investigate the lifetime of macroscopic entanglement under the influence of decoherence. For GreenbergerHorneZeilinger type superposition states, we find that the lifetime decreases with the size of the system (i.e., the number of independent degrees of freedom), and the effective number of subsystems that remain entangled decreases with time. For a class of other states (e.g., cluster states), however, we show that the lifetime of entanglement is independent of the size of the system.
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M. Hein, J. Eisert, H. J. Briegel Multiparty entanglement in graph states,
Physical Review A (Atomic, Molecular, and Optical Physics) 69 062311, (2004),
URL doi:10.1103/PhysRevA.69.062311 (ID: 314551)
Toggle Abstract
Graph states are multiparticle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are manybody spin states of distributed quantum systems that play a significant role in quantum error correction, multiparty quantum communication, and quantum computation within the framework of the oneway quantum computer. We characterize and quantify the genuine multiparticle entanglement of such graph states in terms of the Schmidt measure, to which we provide upper and lower bounds in graph theoretical terms. Several examples and classes of graphs will be discussed, where these bounds coincide. These examples include trees, cluster states of different dimensions, graphs that occur in quantum error correction, such as the concatenated [7,1,3]CSS code, and a graph associated with the quantum Fourier transform in the oneway computer. We also present general transformation rules for graphs when local Pauli measurements are applied, and give criteria for the equivalence of two graphs up to local unitary transformations, employing the stabilizer formalism. For graphs of up to seven vertices we provide complete characterization modulo local unitary transformations and graph isomorphisms.
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W. Dür, R. Raussendorf, V. Kendon, H. J. Briegel Quantum random walks in optical lattices,
Phys. Rev. A 66 (2002),
URL (ID: 511606)
Toggle Abstract
We propose an experimental realization of discrete quantum walks using neutral atoms trapped in optical lattices. The quantum walk is taking place in position space and experimental implementation with presentday technology—even using existing setups—seems feasible. We analyze the influence of possible imperfections in the experiment and investigate the transition from a quantum walk to the classical random walk for increasing errors and decoherence.

H. Aschauer, H. J. Briegel Private entanglement over arbitrary distances, even using a noisy apparatus,
88 (2002),
URL (ID: 511607)
Toggle Abstract
We give a security proof of quantum cryptography based entirely on entanglement purification. Our proof applies to all possible attacks (individual and coherent). It implies the security of cryptographic keys distributed with the help of entanglementbased quantum repeaters. We prove the security of the obtained quantum channel which may not be used only for quantum key distribution, but also for secure, albeit noisy, transmission of quantum information.

H. Aschauer, H. J. Briegel A security proof for quantum cryptography based entirely on entanglement purification,
Phys. Rev. B 66 (2002),
URL (ID: 511608)
Toggle Abstract
We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. In the security regime, the purification process factorizes the overall initial state into a tensorproduct state of Alice and Bob, on one side, and Eve on the other side, thus establishing a completely private, albeit noisy, quantum communication channel between Alice and Bob. The security regime is found to coincide for all practical purposes with the purification regime of a twoway recurrence protocol. This makes twoway entanglement purification protocols, which constitute an important element in the quantum repeater, an efficient tool for secure longdistance quantum cryptography.

R. Raussendorf, H. J. Briegel Computational model for the oneway quantum computer: Concepts and Summary,
Eprint quantph (2002),
arXiv:quantph/0207183v1 (ID: 537006)
Toggle Abstract
The oneway quantum computer (QCc) is a universal scheme of quantum computation consisting only of onequbit measurements on a particular entangled multiqubit state, the cluster state. The computational model underlying the QCc is different from the quantum logic network model and it is based on different constituents. It has no quantum register and does not consist of quantum gates. The QCc is nevertheless quantum mechanical since it uses a highly entangled cluster state as the central physical resource. The scheme works by measuring quantum correlations of the universal cluster state.

R. Raussendorf, H. J. Briegel Computational model underlying the oneway quantum computer,
Quantum Information and Computation 2 6 433, (2002),
arXiv:quantph/0108067v2 (ID: 537007)
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In this paper we present the computational model underlying the oneway quantum computer which we introduced recently [Phys. Rev. Lett. 86, 5188 (2001)]. The oneway quantum computer has the property that any quantum logic network can be simulated on it. Conversely, not all ways of quantum information processing that are possible with the oneway quantum computer can be understood properly in network model terms. We show that the logical depth is, for certain algorithms, lower than has so far been known for networks. For example, every quantum circuit in the Clifford group can be performed on the oneway quantum computer in a single step.

H. Aschauer, H. J. Briegel Der Quantenfingerabdruck,
Physik Journal 1 22 (2002),
(ID: 537011)

H. Aschauer, H. J. Briegel Quantum communication and decoherence,
Eprint quantph (2002),
arXiv:quantph/0208014v2 (ID: 537014)
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In this contribution we will give a brief overview on the methods used to overcome decoherence in quantum communication protocols. We give an introduction to quantum error correction, entanglement purification and quantum cryptography. It is shown that entanglement purification can be used to create ``private entanglement'', which makes it a useful tool for cryptographic protocols.

R. Raussendorf, D. Browne, H. J. Briegel The oneway quantum computer  a nonnetwork model of quantum computation,
Journal of Modern Optics 49 (2002),
(ID: 537015)

H. Aschauer, H. J. Briegel Entanglement purification with noisy apparatus can be used to factor out an eavesdropper,
Eur. Phys. J. D 18 171, (2002),
DOI:10.1140/epjd/e20020021 (ID: 537016)
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We give a proof that entanglement purification, even with noisy apparatus, is sufficient to disentangle an eavesdropper (Eve) from the communication channel. Our proof applies to all possible attacks (individual and coherent). Due to the quantum nature of the entanglement purification protocol, it is also possible to use the obtained quantum channel for secure transmission of quantum information.