Geometry of quantum correlations in space-time

TL;DR

This paper unifies the geometric description of quantum correlations in space and time, revealing a symmetric structure that is broken by non-unital channels, and identifies temporal correlations similar to bipartite entanglement.

Contribution

It introduces a unified geometric framework for analyzing two-point quantum correlations in space-time, bridging spatial and temporal quantum correlations.

Findings

Symmetric structure between space and time correlations.

Non-unital channels break the symmetry.

Temporal correlations can mimic bipartite entanglement.

Abstract

The traditional formalism of non-relativistic quantum theory allows the state of a quantum system to extend across space, but only restricts it to a single instant in time, leading to distinction between theoretical treatments of spatial and temporal quantum correlations. Here we unify the geometrical description of two-point quantum correlations in space-time. Our study presents the geometry of correlations between two sequential Pauli measurements on a single qubit undergoing an arbitrary quantum channel evolution together with two-qubit spatial correlations under a common framework. We establish a symmetric structure between quantum correlations in space and time. This symmetry is broken in the presence of non-unital channels, which further reveals a set of temporal correlations that are indistinguishable from correlations found in bipartite entangled states.