Admissible Causal Structures and Causal Inequalities

Being at the core of many physical theories, often as a self-evident pre-supposition, the notion of global time carries through to the theory implicit assumptions, e.g., that events are causally ordered. More specifically, in quantum theory time appears as an intrinsic parameter from which the causal ordering of the events follows. In a theory where only the local validity of quantum theory is assumed, see [1], the nature of ``space-time'' is encoded in the signalling relations among the different local labs, where the agents perform quantum experiments. The local labs can be thought of as the local space-time regions. But what are the possible signalling relations among them if quantum mechanics is (locally) valid in each? We find a graph-theoretic criterion that singles out all such causal structures for unitarily extensible processes [2]. Moreover, we show that quantum theory does not allow for causal structures impossible with classical-deterministic theories [3]. Finally, we provide two graph-theoretic criteria from which, in the classical-deterministic case, non-violations and violations of causal inequalities follow.

[1]  Ognyan Oreshkov, Fabio Costa, and Časlav Brukner. "Quantum correlations with no causal order", Nature Communications, 3:1092, Oct 2012.

[2] M. Araùjo, A. Feix,   M. Navasquès, Č. Brukner, "A purification postulate for quantum mechanics with indefinite causal order", Quantum 1, 10 (2017).

[3] Ä. Baumeler and S. Wolf, Device-independent test of causal order and relations to fixed-points, New Journal of Physics 18, 035014 (2016).

[4] Jonathan Barrett, Robin Lorenz, and Ognyan Oreshkov. "Cyclic quantum causal models", preprint arXiv:2002.12157 [quant-ph], 2020

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