Spin quantum correlations of relativistic particles

TL;DR

This paper investigates how relativistic effects influence quantum entanglement and Bell inequality violations in spin-1/2 particles, revealing frame-dependent violations and the importance of momentum considerations.

Contribution

It demonstrates that relativistic particles cannot always maximally violate Bell inequalities without momentum post-selection, highlighting the frame dependence of quantum correlations.

Findings

Bell inequality violation depends on particle velocity and reference frame.

Maximal violation requires momentum post-selection in relativistic systems.

Frame dependence can suppress Bell inequality violations.

Abstract

We show that a pair of massive relativistic spin-1/2 particles prepared in a maximally entangled spin state in general is not capable of maximally violating the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a post-selection of the particles momenta, representing a major difference in relation to non-relativistic systems. This occurs because the quantization axis of the measurements performed on each particle depends on the particle velocity, such that it is not possible to define a reduced density matrix for the particles spin. We also show that the amount of violation of the CHSH inequality depends on the reference frame, and that in some frames the inequality may not be violated.