Time-asymmetry and causal structure

TL;DR

This paper explores how time-reversal of certain devices affects their signaling capabilities, revealing asymmetries that challenge traditional causal structure models and impact quantum information theory in relativistic contexts.

Contribution

It demonstrates that time-reversal can induce signaling in devices with hidden variables, challenging assumptions about symmetric causal structures in quantum theory.

Findings

Time-reversal can turn non-signaling devices into signaling ones.

PR boxes exhibit signaling under time-reversal but not perfect channels.

Results challenge the representation of causal structures as partial orders.

Abstract

We consider devices with two inputs and two outputs, Alice and Bob each having access to one input and one output. To such a device we associate time-reverses by exchanging the roles of the inputs and the outputs. We find that there are devices which admit a local hidden variable representation, but for which time-reverses enable perfect signaling between Alice and Bob. That is, a `perfect channel in one time direction' becomes a `non-channel in the other direction'. Also, for PR boxes time-reverses enable signaling between Alice and Bob, but never as a perfect channel. These results undermine the representation of causal structures as partial orders or similar `time-symmetric structures', as is often assumed in search of a theory of quantum gravity. They also provide new insights into the structure of the polytope of generalized probabilistic correlations, and contribute to the growing area of research into quantum information processing in relativistic spacetimes.