What are temporal correlations

TL;DR

This paper demonstrates that quantum temporal correlations are fundamentally equivalent to spatial correlations, providing a rigorous framework and methods for their complete characterization and classification.

Contribution

It introduces a formal proof linking temporal and spatial quantum correlations and offers procedures for their full determination and classification.

Findings

Temporal correlations are equivalent to spatial correlations in quantum mechanics.

Temporal correlations can be represented as quantum channels.

The paper provides methods to fully determine and classify quantum temporal correlations.

Abstract

Space and time are crucial twins in physics. In quantum mechanics, spatial correlations already reveal nonclassical features, such as entanglement, and have bred many quantum technologies. However, the nature of quantum temporal correlations still remains in vague. In this Letter, based on the entangled-history formalism, we prove rigorously that temporal correlations are equivalent to spatial correlations. The effect of temporal correlations corresponds to a quantum channel. The resulting quantifications and classifications of quantum temporal correlations are illustrated in a natural way. Our proposed procedures also show how to determine temporal correlations completely.