Measurement-and-Repreparation Operations and Causal Separability for Two Laboratories

Seminar

In their paper [1]O. Oreshkov et. al. show that the most general quantum correlations between two closed laboratories allow for indenite global causal structures. The two closed laboratories are described by standard quantum mechanics and therefore correspond to sets of quantum instruments. Global causal structures into which the two laboratories are embedded are encoded in so called process matrices. Causally separable process matrices are always compatible with the concept of a denite global causal structure. If the two laboratories are restricted to classical operations the process matrices of interest are all diagonal. In this case one can prove (see supplementary information of [1]) that they are causally separable. Hence, correlations between two classical laboratories can always be understood in terms of a denite global causal structure, such as spacetime. As it turns out this proof can be extended to certain process matrices, which are only partially diagonal, which means diagonal in certain subspaces. Partially diagonal process matrices correspond to so called semiquantum laboratories and correlations. They are compatible with a denite global causal structure, if and only if the information gained from the input in both laboratories can be understood classically. [1] Ognyan Oreshkov, Fabio Costa, and Caslav Brukner. Quantum correlations with no causal order. Nature Communications, 3:1092, 2012.

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