Vilasini Venkatesh R - Compatibility between quantum information-theoretic and spatio-temporal causal structures: no-go results for indefinite causality

Compatibility between quantum information-theoretic and spatio-temporal causal structures: no-go results for indefinite causality

This seminar, given by Vilasini Venkatesh R, will happend on 05 October 2023, at 14:0. It will take place in Room 405 24/25 .

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Abstract

Causality can be defined in terms of a spatio-temporal structure or based on information-theoretic concepts such as agents’ interventions and observable correlations. The process matrix framework describes quantum indefinite causal structures in the information-theoretic sense, but the physicality of such processes remains an open question. At the same time, there are several experiments that claim to implement such processes in Minkowski space-time, which presents an apparent paradox: how can an indefinite information-theoretic causal structure be compatible with relativistic causality in a definite spacetime causal structure? We develop a general theoretical framework for addressing such issues, which formulates the compatibility between these two causality notions, even in scenarios where quantum systems are not necessarily localised in spacetime. First, we characterise information-theoretic causality purely operationally in terms of the signalling structure which agents can infer by performing interventions on a (possibly cyclic) quantum network. By embedding these in a background space-time, we formulate relativistic causality principles such as the impossibility of superluminal signalling. This framework leads to several no-go theorems for the realisations of process matrices in a space-time, showing in particular that indefiniteness of causal order in the process framework translates to the non-localisation of information in the space-time. Moreover, we resolve the apparent paradox by introducing the concept of fine-graining and showing that any realisation of an indefinite causal order process satisfying relativistic causality in a background space-time will ultimately admit a fine-grained description in terms of a definite and acyclic information-theoretic causal structure that is consistent with the light-cone structure of the spacetime. This approach enables a characterisation of the set of quantum processes realisable in Minkowski spacetime, which indicates that causal inequality violating processes cannot be physically realised in a fixed spacetime in a non-trivial manner. Related references: V. Vilasini and R. Renner https://arxiv.org/abs/2203.11245 V. Vilasini, L. del Rio, R. Renner (in preparation) partly based on QPL 2020 talk: https://wdi.centralesupelec.fr/users/valiron/qplmfps/papers/qs01t3.pdf M. Salzger and V. Vilasini (in preparation) based on MS’s master’s thesis https://arxiv.org/abs/2304.06735