Non-classicality of temporal correlations

TL;DR

This paper explores the non-classical nature of temporal correlations in quantum systems, showing that certain quantum measurement sequences cannot be simulated classically, highlighting fundamental differences from spatial correlations.

Contribution

It introduces a formal definition of non-classical temporal correlations and demonstrates that some quantum measurement sequences defy classical simulation even with unlimited memory.

Findings

Temporal correlations between projective measurements on a qubit are classically simulable.

Certain sequences of POVM measurements on an m-level system are not classically simulable.

The results distinguish non-classical temporal correlations from classical models.

Abstract

The results of space-like separated measurements are independent of distant measurement settings, a property one might call two-way no-signalling. In contrast, time-like separated measurements are only one-way no-signalling since the past is independent of the future but not vice-versa. For this reason temporal correlations that are formally identical to non-classical spatial correlations can still be modelled classically. We define non-classical temporal correlations as the ones which cannot be simulated by propagating in time a classical information content of a quantum system. We first show that temporal correlations between results of any projective quantum measurements on a qubit can be simulated classically. Then we present a sequence of POVM measurements on a single $m$-level quantum system that cannot be explained by propagating in time $m$-level classical system and using classical computers with unlimited memory.