Quantum correlations in the temporal CHSH scenario

TL;DR

This paper explores quantum correlations in a temporal CHSH scenario, revealing fundamental limits, including the Tsirelson bound, limited signaling capacity, and a temporal Hardy paradox, highlighting the differences from spatial correlations.

Contribution

It establishes that temporal quantum correlations are constrained similarly to spatial ones and derives new bounds and paradoxes specific to the temporal setting.

Findings

Quantum correlations in temporal CHSH mirror spatial scenario constraints.

Tsirelson bound validity and PR-box impossibility confirmed.

Maximal signaling capacity is approximately 0.32 bits.

Abstract

We consider a temporal version of the CHSH scenario using projective measurements on a single quantum system. It is known that quantum correlations in this scenario are fundamentally more general than correlations obtainable with the assumptions of macroscopic realism and non-invasive measurements. In this work, we also educe some fundamental limitations of these quantum correlations. One result is that a set of correlators can appear in the temporal CHSH scenario if and only if it can appear in the usual spatial CHSH scenario. In particular, we derive the validity of the Tsirelson bound and the impossibility of PR-box behavior. The strength of possible signaling also turns out to be surprisingly limited, giving a maximal communication capacity of approximately 0.32 bits. We also find a temporal version of Hardy's nonlocality paradox with a maximal quantum value of 1/4.