Bell-type inequalities for systems of relativistic vector bosons

TL;DR

This paper analyzes the violation of Bell-type inequalities in systems of relativistic vector bosons, revealing that certain inequalities can be violated depending on the state and relative speed of particles.

Contribution

It identifies two classes of scalar states in vector boson-antiboson systems and explores their potential to violate Mermin and CGLMP inequalities, considering relativistic effects.

Findings

Mermin and CGLMP inequalities can be violated in some scalar states.

Violation depends on the relative speed of the particles.

Generalized CHSH inequality is not violated for these states.

Abstract

We perform a detailed analysis of the possible violation of various Bell-type inequalities for systems of vector boson-antiboson pairs. Considering the general case of an overall scalar state of the bipartite system, we identify two distinct classes of such states, and determine the joint probabilities of spin measurement outcomes for each them. We calculate the expectation values of the CHSH, Mermin and CGLMP inequalities and find that while the generalised CHSH inequality is not expected to be violated for any of the scalar states, in the case of the Mermin and CGLMP inequalities the situation is different -- these inequalities can be violated in certain scalar states while they cannot be violated in others. Moreover, the degree of violation depends on the relative speed of the two particles.