On a class of bounded Hermitian operators for the Bell-CHSH inequality in Quantum Field Theory

TL;DR

This paper introduces a class of bounded Hermitian operators based on Weyl operators to analyze Bell-CHSH inequality violations in relativistic quantum field theory, combining analytic and numerical methods.

Contribution

It presents a novel set of bounded Hermitian operators for Bell tests in quantum field theory, utilizing modular theory and explicit test function construction for localization.

Findings

Operators enable both analytic and numerical analysis of Bell violations.

Application to 1+1 Minkowski spacetime causal diamonds.

Insights into relativistic quantum correlations.

Abstract

The violation of the Bell-CHSH inequality in a relativistic scalar Quantum Field Theory is analysed by means of a set of bounded Hermitian operators constructed out of the unitary Weyl operators. These operators allow for both analytic and numerical approaches. While the former relies on the modular theory of Tomita-Takesaki, the latter is devised through an explicit construction of the test functions needed for the localization of the aforementioned operators. The case of causal tangent diamonds in $1+1$ Minkowski spacetime is scrutinized.