Inferring the arrow of time in quantum spatiotemporal correlations

TL;DR

This paper introduces a method to infer the temporal order of quantum measurements by analyzing spatiotemporal correlations, utilizing a novel recovery map to distinguish forward and reverse quantum processes.

Contribution

It presents a new protocol for determining the arrow of time in quantum experiments using pseudo density matrices and a novel recovery map for inverting unitary dilations.

Findings

The protocol can distinguish between symmetric and asymmetric time conditions.

It successfully identifies the directionality of quantum processes in simulated scenarios.

The approach adapts to different quantum state representations like Leifer-Spekkens states.

Abstract

We consider how to tell the time-ordering associated with measurement data from quantum experiments at two times and any number of qubits. We define an arrow of time inference problem. We consider conditions on the initial and final states that are symmetric or asymmetric under time reversal. We represent the spatiotemporal measurement data via the pseudo density matrix space-time state. There is a forward process which is CPTP and a reverse process which is obtained via a novel recovery map based on inverting unitary dilations. For asymmetric conditions, the protocol determines whether the data is consistent with the unitary dilation recovery map or the CPTP map. For symmetric conditions, the recovery map yields a valid CPTP map and the experiment may have taken place in either direction. We also discuss adapting the approach to the Leifer-Spekkens or Process matrix space-time states.