Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory

TL;DR

This paper develops a numerical method to analyze Bell-CHSH inequality violations in relativistic quantum fields, revealing mass-dependent violations in the vacuum state using Lorentz-invariant test functions.

Contribution

It introduces a numerical framework for evaluating Bell-CHSH inequalities in quantum field theory using smeared fields and Lorentz-invariant inner products.

Findings

Violations of Bell-CHSH inequality observed for various particle masses.

Numerical framework effectively computes Lorentz-invariant inner products.

Causality verified through numerical evaluation of the Pauli-Jordan function.

Abstract

The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. A numerical framework for these inner products is devised. Causality is also explicitly checked by a numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter.