Monogamy of quantum entanglement in time

TL;DR

This paper explores the structure of temporal quantum correlations, revealing a monogamy property similar to spatial entanglement, using the entangled histories framework and tensor algebra.

Contribution

It introduces a novel analysis of temporal monogamy of entanglement, deriving Tsirelson bounds within the entangled histories approach.

Findings

Temporal correlations differ from spatial ones but show monogamy of entanglement.

Tsirelson bound for temporal Bell inequalities derived from entangled histories.

Tensor algebra is essential for representing evolving quantum systems.

Abstract

In this paper we state a fundamental question about the structure of correlations in time and analyze temporal monogamy relations. We show that the nature of temporal correlations is inherently different from the spatial ones but in similarity to quantum spatial correlations, we expose a phenomenon of monogamy of quantum entanglement in time. We perform this task applying the entangled histories framework as a modifcation of the consistent histories approach. These considerations are supported by introduction of necessary tools specific for the tensor algebra used for representation of spatial correlations. We show that Tsirelson bound on temporal Bell-like inequalities can be derived from the entangled histories approach. Finally, we point out that in a context of the tensor algebra used for linking states in different times further studies on mathematical structure of the state representing evolving systems are needed.