Hi all,
Tomorrow Vilasini will tell us about her work on 'Embedding cyclic causal structures in acyclic spacetimes: no-go results for process matrices'. See below for the abstract. The talk will take place at 2pm in HIT E 41.1 or on Zoom: https://ethz.zoom.us/j/362994444.
Best, Ladina
%%%%%%%%%
Title: Embedding cyclic causal structures in acyclic spacetimes: no-go results for process matrices
V. Vilasini and Renato Renner, based on https://arxiv.org/abs/2203.11245
Abstract: Causality can be defined in terms of a space-time structure or based on information-theoretic structures, which correspond to different notions of causation. 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 in Minkowski spacetime (which gives a definite spacetime notion of causality) that claim to implement indefinite information-theoretic causal structures, suggesting an apparent tension between these notions. To address this, we develop a general framework that disentangles these two notions and characterises their relationship in scenarios where quantum systems are not necessarily localised in spacetime. Formulating (possibly cyclic) quantum causal structures in terms of a composition of quantum maps through feedback loops, we proceed to describe their embedding in acyclic background spacetimes. Then relativistic causality takes the form of a compatibility condition between the information-theoretic and spacetime causal order relations. Connecting the process matrix formalism to cyclic causal structures with a focus on causal relations that can be inferred operationally through agents’ interventions, we derive a number of no-go results for physical realisations of process matrices in a spacetime. In particular, this reveals that it is impossible to physically realise indefinite causal order processes with spacetime localised systems. Further, we show that any realisation of an indefinite causal order process respecting relativistic causality in a background spacetime ultimately admits a fine-grained description in terms of a definite acyclic information-theoretic causal structure that is consistent with the light-cone structure of the spacetime. This resolves the apparent tension between the two causality notions. Finally, we discuss the operational meaning of indefinite causal structures in light of our results.