Using spatiotemporal Born rule for testing macroscopic realism: some applications to the pseudo-density matrices and nonclassical temporal correlations

TL;DR

This paper introduces a spatiotemporal Born rule approach to test macroscopic realism by analyzing pseudo-density matrices, revealing that deviations from classical predictions indicate nonclassical temporal correlations and temporal entanglement.

Contribution

It proposes a novel framework linking spatiotemporal Born rule, pseudo-density matrices, and macroscopic realism, including a new definition of temporal entanglement.

Findings

Deviations from L"uders distribution indicate violation of macroscopic realism.

Temporal entanglement is necessary for violation of temporal Bell inequalities.

Negativity of PDM correlates with temporal entanglement and nonclassical temporal correlations.

Abstract

We show that, given an evolving quantum system and the quasiprobability distribution generated by the spatiotemporal generalization of the Born rule in pseudo density-matrices (PDMs), this distribution deviates from the sequential measurements probability distribution, given by the L\"uders von-Neumann distribution, if and only if the non-signaling in time (NSIT) is violated; equivalently, if and only if the macroscopic realism (MR) is violated. Furthermore, we propose a definition of temporal entanglement according to the structure of the PDMs that is analogous to the definition of spatial entanglement in density matrices, showing that temporal entanglement is necessary for the violation of temporal Bell inequalities and the violation of MR. We employ our results to study the relationship between the negativity of the PDM, temporal entanglement, violation of temporal Bell inequalities, and MR.