Device-independent test of causal order and relations to fixed-points

Abstract

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order between a set of parties, together with free randomness, implies device-independent inequalities --- just as the assumption of locality does. It is known that local validity of quantum theory is consistent with violating such inequalities. Moreover, for three parties or more, even the (stronger) assumption of local classical probability theory plus logical consistency allows for violating causal inequalities. Here, we show that a classical environment (with which the parties interact), possibly containing loops, is logically consistent if and only if whatever the involved parties do, there is exactly one fixed-point, the latter being representable as a mixture of deterministic fixed-points. We further show that the non-causal view allows for a model of computation strictly more powerful than computation in a world of fixed causal orders.

24 pages, 8 figures, 4 tables

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• Unlimited non-causal correlations and their relation to non-locality
• Process Products Need Qualification
• Non-causal computation
• Admissible Causal Structures and Correlations
• Equivalence of Grandfather and Information Antinomy Under Intervention
• Trading causal order for locality
• Exploring the limits of no backward in time signalling
• The Möbius game and other Bell tests for relativity
• Bell Correlations and the Common Future
• Error-free interconversion of nonlocal boxes
• Tripartite non-classical correlations without backwards in time signalling
• Classical and Quantum Query Complexity of Boolean Functions under Indefinite Causal Order
• Anomalous non-classicality via correlative and entropic Bell inequalities