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C. Kargi, J. P. Dehollain, F. Henriques, L. Sieberer, T. Olsacher, P. Hauke, M. Heyl, P. Zoller, N. Langford Quantum Chaos and Trotterisation Thresholds in Digital Quantum Simulations,
Quantum 9 (2025-12-02),
http://dx.doi.org/10.22331/q-2025-12-02-1924 doi:10.22331/q-2025-12-02-1924
Digital quantum simulation (DQS) is one of the most promising paths for achieving first useful real-world applications for quantum processors. Yet even assuming rapid progress in device engineering and development of fault-tolerant quantum processors, algorithmic resource optimisation will long remain crucial to exploit their full power. Currently, Trotterisation provides state-of-the-art DQS resource scaling. Moreover, recent theoretical studies of Trotterised Ising models suggest it also offers feasible performance for unexpectedly large step sizes up to a sharp breakdown threshold, but demonstrations and characterisation have been limited, and the question of whether this behaviour applies as a general principle has remained open. Here, we study a set of paradigmatic and experimentally realisable DQS models, and show that a range of Trotterisation performance behaviours, including the existence of a sharp threshold, are remarkably universal. Carrying out a detailed characterisation of a range of performance signatures, we demonstrate that it is the onset of digitisation-induced quantum chaos at this threshold that underlies the breakdown of Trotterisation. Specifically, combining analysis of detailed dynamics with conclusive, global static signatures based on random matrix theory, we observe clear signatures of regular behaviour pre-threshold, and conclusive, initial-state-independent evidence for the onset of quantum chaotic dynamics beyond the threshold. We also show how this behaviour consistently emerges as a function of system size for sizes and times already relevant for current experimental DQS platforms. The advances in this work open up many important questions about the algorithm performance and general shared features of sufficiently complex Trotterisation-based DQS. Answering these will be crucial for extracting the maximum simulation power from future quantum processors.
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C. Tabares, C. Kokail, P. Zoller, D. Gonzalez Cuadra, A. Gonzalez-Tudela Programming optical-lattice Fermi-Hubbard quantum simulators,
PRX Quantum 6 30356 (2025-09-19),
http://dx.doi.org/10.1103/3nx4-bnyy doi:10.1103/3nx4-bnyy
Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local control of chemical potentials and tunnelings, and thus enable to operate this platform digitally as a programmable quantum simulator. Here, we explore these opportunities and develop ground-state preparation algorithms for different fermionic models, based on the ability to implement both single-particle and many-body, high-fidelity fermionic gates, as provided by the native FH Hamiltonian. In particular, we first design variational, pre-compiled quantum circuits to prepare the ground state of the natively implemented FH model, with significant speedups relative to competing adiabatic protocols. Besides, the versatility of this variational approach enables to target extended FH models, i.e., including terms that are not natively realized on the platform. As an illustration, we include next-nearest-neighbor tunnelings at finite dopings, relevant in the context of -wave superconductivity. Furthermore, we discuss how to approximate the imaginary-time evolution using variational fermionic circuits, both as an alternative state-preparation strategy, and as a subroutine for the Quantum Lanczos algorithm to further improve the energy estimation. We benchmark our protocols for ladder geometries, though they can be readily applied to 2D experimental setups to address regimes beyond the capabilities of current classical methods. These results pave the way for more efficient and comprehensive explorations of relevant many-body phases with existing programmable fermionic quantum simulators.
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R. Ott, T. Zache, N. Maskara, M. Lukin, P. Zoller, H. Pichler Probing topological entanglement on large scales,
Phys. Rev. Lett. 135 90401 (2025-08-25),
http://dx.doi.org/10.1103/mdsf-wrbj doi:10.1103/mdsf-wrbj
Topologically ordered quantum matter exhibits intriguing long-range patterns of entanglement, which reveal themselves in subsystem entropies. However, measuring such entropies, which can be used to certify topological order, on large partitions is challenging and becomes practically unfeasible for large systems. We propose a protocol based on local adiabatic deformations of the Hamiltonian which extracts the universal features of long-range topological entanglement from measurements on small subsystems of finite size, trading an exponential number of measurements against a polynomial-time evolution. Our protocol is general and readily applicable to various quantum simulation architectures. We apply our method to various string-net models representing both abelian and non-abelian topologically ordered phases, and illustrate its application to neutral atom tweezer arrays with numerical simulations.
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R. Ott, D. González-Cuadra, T. Zache, P. Zoller, A. Kaufman, H. Pichler Error-corrected fermionic quantum processors with neutral atoms,
Phys. Rev. Lett. 135 90601 (2025-08-25),
http://dx.doi.org/10.1103/zkpl-hh28 doi:10.1103/zkpl-hh28
Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where non-local fermionic statistics are guaranteed at the hardware level. Implementing quantum error correction in this setup is however challenging, due to the atom-number superselection present in atomic systems, that is, the impossibility of creating coherent superpositions of different particle numbers. In this work, we overcome this constraint and present a blueprint for an error-corrected fermionic quantum computer that can be implemented using current experimental capabilities. To achieve this, we first consider an ancillary set of fermionic modes and design a fermionic reference, which we then use to construct superpositions of different numbers of referenced fermions. This allows us to build logical fermionic modes that can be error corrected using standard atomic operations. Here, we focus on phase errors, which we expect to be a dominant source of errors in neutral-atom quantum processors. We then construct logical fermionic gates, and show their implementation for the logical particle-number conserving processes relevant for quantum simulation. Finally, our protocol is illustrated using a minimal fermionic circuit, where it leads to a quadratic suppression of the logical error rate.
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A. Kruckenhauser, M. Yuan, H. Zheng, M. Mamaev, P. Zeng, X. M. Mao, Q. Xu, T. Zache, L. Jiang, R. van Bijnen, P. Zoller Dark spin-cats as biased qubits,
Phys. Rev. Lett. 135 20601 (2025-07-08),
http://dx.doi.org/10.1103/w9zh-jwsx doi:10.1103/w9zh-jwsx
We present a biased atomic qubit, universally implementable across all atomic platforms, encoded as a `spin-cat' within ground state Zeeman levels. The key characteristic of our configuration is the coupling of the ground state spin manifold of size Fg≫1 to an excited Zeeman spin manifold of size Fe=Fg−1 using light. This coupling results in eigenstates of the driven atom that include exactly two dark states in the ground state manifold, which are decoupled from light and immune to spontaneous emission from the excited states. These dark states constitute the `spin-cat', leading to the designation `dark spin-cat'. We demonstrate that under strong Rabi drive and for large Fg, the `dark spin-cat' is autonomously stabilized against common noise sources and encodes a qubit with significantly biased noise. Specifically, the bit-flip error rate decreases exponentially with Fg relative to the dephasing rate. We provide an analysis of dark spin-cats, their robustness to noise, and discuss bias-preserving single qubit and entangling gates, exemplified on a Rydberg tweezer platform.
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D. Gonzalez Cuadra, M. Hamdan, T. Zache, B. Braverman, M. Kornjaca, A. Lukin, S. H. Cantu, F. Liu, S. Wang, A. Keesling, M. Lukin, P. Zoller, A. Bylinskii Observation of string breaking on a (2 + 1)D Rydberg quantum simulator,
Nature 462 326 (2025-06-04),
http://dx.doi.org/10.1038/s41586-025-09051-6 doi:10.1038/s41586-025-09051-6
Lattice gauge theories (LGTs) describe a broad range of phenomena in condensed matter and particle physics. A prominent example is confinement, responsible for bounding quarks inside hadrons such as protons or neutrons. When quark-antiquark pairs are separated, the energy stored in the string of gluon fields connecting them grows linearly with their distance, until there is enough energy to create new pairs from the vacuum and break the string. While such phenomena are ubiquitous in LGTs, simulating the resulting dynamics is a challenging task. Here, we report the observation of string breaking in synthetic quantum matter using a programmable quantum simulator based on neutral atom arrays. We show that a (2+1)D LGT with dynamical matter can be efficiently implemented when the atoms are placed on a Kagome geometry, with a local U(1) symmetry emerging from the Rydberg blockade, while long-range Rydberg interactions naturally give rise to a linear confining potential for a pair of charges, allowing us to tune both their masses as well as the string tension. We experimentally map out the corresponding phase diagram by adiabatically preparing the ground state of the atom array in the presence of defects, and observe substructure of the confined phase, distinguishing regions dominated by fluctuating strings or by broken string configurations. Finally, by harnessing local control over the atomic detuning, we quench string states and observe string breaking dynamics exhibiting a many-body resonance phenomenon. Our work paves a way to explore phenomena in high-energy physics using programmable quantum simulators.
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M. Meth, J. Haase, J. Zhang, C. Edmunds, L. Postler, A. Steiner, A. Jena, L. Dellantonio, R. Blatt, P. Zoller, T. Monz, P. Schindler, C. A. Muschik, M. Ringbauer Simulating 2D lattice gauge theories on a qudit quantum computer,
Nature Phys. 21 576 (2025-03-25),
http://dx.doi.org/10.1038/s41567-025-02797-w doi:10.1038/s41567-025-02797-w
Particle physics describes the interplay of matter and forces through gauge theories. Yet, the intrinsic quantum nature of gauge theories makes important problems notoriously difficult for classical computational techniques. Quantum computers offer a promising way to overcome these roadblocks. We demonstrate two essential requirements on this path: first, we perform a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. Second, we show how to refine the gauge-field discretization beyond its minimal representation, using a trapped-ion qudit quantum processor, where quantum information is encoded in several states per ion. Such qudits are ideally suited for describing gauge fields, which are naturally high dimensional, leading to reduced register size and circuit complexity. We prepare the ground state of the model using a variational quantum eigensolver and observe the effect of dynamical matter on quantized magnetic fields. By controlling the qudit dimension, we also show how to seamlessly observe the effect of different gauge-field truncations. Finally, we experimentally study the dynamics of pair creation and magnetic energy. Our results open the door for hardware-efficient quantum simulations of gauge theories with qudits in near-term quantum devices.
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A. Chu, V. Martinez-Lahuerta, M. Miklos, K. Kim, P. Zoller, K. Hammerer, J. Ye, A. M. Rey Exploring the Dynamical Interplay between Mass-Energy Equivalence, Interactions, and Entanglement in an Optical Lattice Clock,
Phys. Rev. Lett. 134 93201 (2025-03-03),
http://dx.doi.org/10.1103/PhysRevLett.134.093201 doi:10.1103/PhysRevLett.134.093201
We propose protocols that probe manifestations of the mass-energy equivalence in an optical lattice clock (OLC) interrogated with spin coherent and entangled quantum states. To tune and uniquely distinguish the mass-energy equivalence effects (gravitational redshift and second order Doppler shift) in such setting, we devise a dressing protocol using an additional nuclear spin state. We then analyze the interplay between photon-mediated interactions and gravitational redshift and show that such interplay can lead to entanglement generation and frequency synchronization. In the regime where all atomic spins synchronize, we show the synchronization time depends on the initial entanglement of the state and can be used as a proxy of its metrological gain compared to a classical state. Our work opens new possibilities for exploring the effects of general relativity on quantum coherence and entanglement in OLC experiments.
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T. Olsacher, T. Kraft, C. Kokail, B. Kraus, P. Zoller Hamiltonian and Liouvillian learning in weakly-dissipative quantum many-body systems,
Quantum Sci. Technol. 10 15065 (2025-01-08),
http://dx.doi.org/10.1088/2058-9565/ad9ed5 doi:10.1088/2058-9565/ad9ed5
We discuss Hamiltonian and Liouvillian learning for analog quantum simulation from non-equilibrium quench dynamics in the limit of weakly dissipative many-body systems. We present various strategies to learn the operator content of the Hamiltonian and the Lindblad operators of the Liouvillian. We compare different ansätze based on an experimentally accessible "learning error" which we consider as a function of the number of runs of the experiment. Initially, the learning error decreasing with the inverse square root of the number of runs, as the error in the reconstructed parameters is dominated by shot noise. Eventually the learning error remains constant, allowing us to recognize missing ansatz terms. A central aspect of our approach is to (re-)parametrize ansätze by introducing and varying the dependencies between parameters. This allows us to identify the relevant parameters of the system, thereby reducing the complexity of the learning task. Importantly, this (re-)parametrization relies solely on classical post-processing, which is compelling given the finite amount of data available from experiments. A distinguishing feature of our approach is the possibility to learn the Hamiltonian, without the necessity of learning the complete Liouvillian, thus further reducing the complexity of the learning task. We illustrate our method with two, experimentally relevant, spin models.
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T. Kraft, M. K. Joshi, W. LAM, T. Olsacher, F. Kranzl, J. Franke, L. K. Joshi, R. Blatt, A. Smerzi, D. S. França, B. Vermersch, B. Kraus, C. F. Roos, P. Zoller Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning,
(2025-11-28),
arXiv:2511.23392 arXiv:2511.23392
Analog Quantum Simulators offer a route to exploring strongly correlated many-body dynamics beyond classical computation, but their predictive power remains limited by the absence of quantitative error estimation. Establishing rigorous uncertainty bounds is essential for elevating such devices from qualitative demonstrations to quantitative scientific tools. Here we introduce a general framework for bounded-error quantum simulation, which provides predictions for many-body observables with experimentally quantifiable uncertainties. The approach combines Hamiltonian and Lindbladian Learning--a statistically rigorous inference of the coherent and dissipative generators governing the dynamics--with the propagation of their uncertainties into the simulated observables, yielding confidence bounds directly derived from experimental data. We demonstrate this framework on trapped-ion quantum simulators implementing long-range Ising interactions with up to 51 ions, and validate it where classical comparison is possible. We analyze error bounds on two levels. First, we learn an open-system model from experimental data collected in an initial time window of quench dynamics, simulate the corresponding master equation, and quantitatively verify consistency between theoretical predictions and measured dynamics at long times. Second, we establish error bounds directly from experimental measurements alone, without relying on classical simulation--crucial for entering regimes of quantum advantage. The learned models reproduce the experimental evolution within the predicted bounds, demonstrating quantitative reliability and internal consistency. Bounded-error quantum simulation provides a scalable foundation for trusted analog quantum computation, bridging the gap between experimental platforms and predictive many-body physics. The techniques presented here directly extend to digital quantum simulation.
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C. Tabares, D. Wild, I. Cirac, P. Zoller, A. Gonzalez-Tudela, D. González-Cuadra Estimating ground-state properties in quantum simulators with global control,
(2025-11-06),
arXiv:2511.04434 arXiv:2511.04434
Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time evolution under a target Hamiltonian. This avoids the need for controlled operations that are typically required in conventional quantum phase estimation and extends the algorithm applicability to analog simulators. Our method extracts energy differences from measurements of the Loschmidt echo over an initial ground-state approximation, combines them with direct energy measurements, and solves a set of equations to infer the individual eigenenergies. We benchmark this protocol on free-fermion systems, showing orders-of-magnitude precision gains over direct energy measurements on the initial state, with accuracy improving rapidly with initial-state fidelity and persisting for hundreds of modes. We further demonstrate applicability to the 2D Ising and Fermi-Hubbard models and show that the approach extends naturally to other observables such as order parameters. Finally, we analyze the effect of experimental imperfections and propose error-mitigation strategies. These results establish a practical route to compute physically relevant quantities with high precision using globally controlled quantum simulators.
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C. Fromonteil, D. Vasilyev, T. Zache, K. Hammerer, A. M. Rey, J. Ye, H. Pichler, P. Zoller Non-local mass superpositions and optical clock interferometry in atomic ensemble quantum networks,
(2025-09-23),
arXiv:2509.19501 arXiv:2509.19501
Quantum networks are emerging as powerful platforms for sensing, communication, and fundamental tests of physics. We propose a programmable quantum sensing network based on entangled atomic ensembles, where optical clock qubits emulate mass superpositions in atom and atom-clock interferometry. Our approach uniquely combines scalability to large atom numbers with minimal control requirements, relying only on collective addressing of internal atomic states. This enables the creation of both non-local and local superpositions with spatial separations beyond those achievable in conventional interferometry. Starting from Bell-type seed states distributed via photonic channels, collective operations within atomic ensembles coherently build many-body mass superpositions sensitive to gravitational redshift. The resulting architecture realizes a non-local Ramsey interferometer, with gravitationally induced phase shifts observable in network-based interference patterns. Beyond extending the spatial reach of mass superpositions, our scheme establishes a scalable, programmable platform to probe the interface of quantum mechanics and gravity, and offers a new experimental pathway to test atom and atom-clock interferometer proposals in a network-based quantum laboratory.
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R. Ott, T. Zache, M. Prüfer, S. Erne, M. Tajik, H. Pichler, J. Schmiedmayer, P. Zoller Hamiltonian Learning in Quantum Field Theories,
Phys. Rev. Research 6 43284 (2024-12-16),
http://dx.doi.org/10.1103/PhysRevResearch.6.043284 doi:10.1103/PhysRevResearch.6.043284
We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for varying spatial measurement resolutions gives access to field theories at different energy scales, and allows to learn a flow of Hamiltonians reminiscent of the renormalization group. Our method, which we demonstrate in both theoretical studies and available data from a quantum gas experiment, promises new ways of addressing the emergence of quantum field theories in quantum simulation experiments.
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H. Kamal, J. Kemp, Y. He, Y. Fuji, M. Aidelsburger, P. Zoller, N. Y. Yao Floquet Flux Attachment in Cold Atomic Systems,
Phys. Rev. Lett. 133 163403 (2024-10-17),
http://dx.doi.org/10.1103/PhysRevLett.133.163403 doi:10.1103/PhysRevLett.133.163403
Flux attachment provides a powerful conceptual framework for understanding certain forms of topological order, including most notably the fractional quantum Hall effect. Despite its ubiquitous use as a theoretical tool, directly realizing flux attachment in a microscopic setting remains an open challenge. Here, we propose a simple approach to realizing flux attachment in a periodically-driven (Floquet) system of either spins or hard-core bosons. We demonstrate that such a system naturally realizes correlated hopping interactions and provides a sharp connection between such interactions and flux attachment. Starting with a simple, nearest-neighbor, free boson model, we find evidence -- from both a coupled wire analysis and large-scale density matrix renormalization group simulations -- that Floquet flux attachment stabilizes the bosonic integer quantum Hall state at 1/4 filling (on a square lattice), and the Halperin-221 fractional quantum Hall state at 1/6 filling (on a honeycomb lattice). At 1/2 filling on the square lattice, time-reversal symmetry is instead spontaneously broken and bosonic integer quantum Hall states with opposite Hall conductances are degenerate. Finally, we propose an optical-lattice-based implementation of our model on a square lattice and discuss prospects for adiabatic preparation as well as effects of Floquet heating.
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B. Vermersch, M. Ljubotina, J. I. Cirac, P. Zoller, M. Serbyn, L. Piroli Many-body entropies and entanglement from polynomially-many local measurements,
Phys. Rev. X 14 31035 (2024-08-26),
http://dx.doi.org/10.1103/PhysRevX.14.031035 doi:10.1103/PhysRevX.14.031035
Randomized measurements (RMs) provide a practical scheme to probe complex many-body quantum systems. While they are a very powerful tool to extract local information, global properties such as entropy or bipartite entanglement remain hard to probe, requiring a number of measurements or classical post-processing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments, and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix which allow us to reconstruct entropies and PT moments from information on local subsystems. Combined with the RM toolbox, this yields a simple strategy for entropy and entanglement estimation which is provably accurate assuming that the state to be measured satisfies the AFCs, and which only requires polynomially-many measurements and post-processing operations. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators, and provide numerical evidence that they are satisfied in more general, physically-interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today's quantum platforms.
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L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, M. K. Joshi Observing the quantum Mpemba effect in quantum simulations,
PRL 133 10402 (2024-07-01),
http://dx.doi.org/10.1103/PhysRevLett.133.010402 doi:10.1103/PhysRevLett.133.010402
The non-equilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this study, we experimentally investigate one of the most puzzling of these phenomena— the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and post-processed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.
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J. Ye, P. Zoller Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics,
Phys. Rev. Lett. 132 190001 (2024-05-07),
http://dx.doi.org/10.1103/PhysRevLett.132.190001 doi:10.1103/PhysRevLett.132.190001
Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today’s realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier.
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R. Stricker, J. Carrasco, M. Ringbauer, L. Postler, M. Meth, C. Edmunds, P. Schindler, R. Blatt, P. Zoller, B. Kraus, T. Monz Towards experimental classical verification of quantum computation,
Quantum Sci. Technol. 9 (2024-02-26),
http://dx.doi.org/10.1088/2058-9565/ad2986 doi:10.1088/2058-9565/ad2986
With today's quantum processors venturing into regimes beyond the capabilities of classical devices [1-3], we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical computers [4,5]. In a recent breakthrough in computer science [6-8], a protocol was developed that allows the verification of the output of a computation performed by an untrusted quantum device based only on classical resources. Here, we follow these ideas, and demonstrate in a first, proof-of-principle experiment a verification protocol using only classical means on a small trapped-ion quantum processor. We contrast this to verification protocols, which require trust and detailed hardware knowledge, as in gate-level benchmarking [9], or additional quantum resources in case we do not have access to or trust in the device to be tested [5]. While our experimental demonstration uses a simplified version [10] of Mahadev's protocol [6] we demonstrate the necessary steps for verifying fully untrusted devices. A scaled-up version of our protocol will allow for classical verification, requiring no hardware access or detailed knowledge of the tested device. Its security relies on post-quantum secure trapdoor functions within an interactive proof [11]. The conceptually straightforward, but technologically challenging scaled-up version of the interactive proofs, considered here, can be used for a variety of additional tasks such as verifying quantum advantage [8], generating [12] and certifying quantum randomness [7], or composable remote state preparation [13].
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J. Carrasco, M. Votto, V. Vitale, C. Kokail, A. Neven, P. Zoller, B. Vermersch, B. Kraus Entanglement phase diagrams from partial transpose moments,
Phys. Rev. A 109 12422 (2024-01-18),
http://dx.doi.org/10.1103/PhysRevA.109.012422 doi:10.1103/PhysRevA.109.012422
We present experimentally and numerically accessible quantities that can be used to differentiate among various families of random entangled states. To this end, we analyze the entanglement properties of bipartite reduced states of a tripartite pure state. We introduce a ratio of simple polynomials of low-order moments of the partially transposed reduced density matrix and show that this ratio takes well-defined values in the thermodynamic limit for various families of entangled states. This allows to sharply distinguish entanglement phases, in a way that can be understood from a quantum information perspective based on the spectrum of the partially transposed density matrix. We analyze in particular the entanglement phase diagram of Haar random states, states resulting form the evolution of chaotic Hamiltonians, stabilizer states, which are outputs of Clifford circuits, Matrix Product States, and fermionic Gaussian states. We show that for Haar random states the resulting phase diagram resembles the one obtained via the negativity and that for all the cases mentioned above a very distinctive behaviour is observed. Our results can be used to experimentally test necessary conditions for different types of mixed-state randomness, in quantum states formed in quantum computers and programmable quantum simulators.