Cat states and violation of the Bell-CHSH inequality in relativistic Quantum Field Theory

TL;DR

This paper demonstrates that a relativistic scalar quantum field theory with a localized cat state can exhibit Bell-CHSH inequality violations, highlighting quantum nonlocality in a relativistic setting.

Contribution

It provides an explicit analytic calculation of Bell-CHSH violation using a localized cat state in relativistic quantum field theory, extending previous non-relativistic results.

Findings

Bell-CHSH correlator evaluated analytically in closed form

Cat states exhibit interference leading to Bell violation

Relativistic quantum field theory can demonstrate quantum nonlocality

Abstract

A cat state localized in the right Rindler wedge is employed to study the violation of the Bell-CHSH inequality in a relativistic scalar free Quantum Field Theory. By means of the bounded Hermitian operator $sign(\varphi(f))$, where $\varphi(f)$ stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.