Are temporal quantum correlations generally non-monogamous?

TL;DR

This paper investigates the unique nature of temporal quantum correlations, revealing a dichotomy where entangled histories are monogamous over time, yet evolving systems violate multi-time Bell inequalities, highlighting a complex temporal entanglement structure.

Contribution

It introduces a novel analysis of temporal quantum correlations, demonstrating the monogamy of entangled histories and deriving bounds for multi-time Bell inequalities.

Findings

Entangled histories are monogamous over time.

Evolving systems violate multi-time Bell inequalities.

Tsirelson bound for temporal correlations is derived.

Abstract

In this paper we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiate them from spatial quantum correlations. We show rigorously that a particular entangled history, which can be associated with a quantum propagator, is monogamous to conserve its consistency throughout time. Yet evolving systems violate monogamous Bell-like multi-time inequalities. This dichotomy, being a novel feature of temporal correlations, has its roots in the measurement process itself which is discussed by means of the bundles of entangled histories. We introduce and discuss a concept of a probabilistic mixture of quantum processes by means of which we clarify why the spatial-like Bell-type monogamous inequalities are further violated. We prove that Tsirelson bound on temporal Bell-like inequalities can be derived from the entangled histories approach and as a generalization, we derive the quantum bound for multi-time Bell-like inequalities. It is also pointed out that what mimics violation of monogamy of temporal entanglement is actually just a kind of polyamory in time but monogamy of entanglement for a particular evolution still holds.