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

TL;DR

This paper explores device-independent tests of causal order, demonstrating that classical environments with loops are logically consistent only if they have a unique fixed-point, and shows non-causal models can outperform fixed-causal computation.

Contribution

It establishes a characterization of classical environments with loops as having a unique fixed-point and links non-causal models to enhanced computational power.

Findings

Classical environments with loops are logically consistent if and only if they have a unique fixed-point.

Non-causal models can perform computations more powerful than fixed causal order models.

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.