Unruh-De Witt detectors, Bell-CHSH inequality and Tomita-Takesaki theory

TL;DR

This paper uses Tomita-Takesaki modular theory to analyze Unruh-De Witt detectors interacting with a scalar field, revealing how quantum field interactions diminish Bell-CHSH inequality violations.

Contribution

It introduces an exact method to evaluate the detector-field system using modular theory, providing new insights into quantum correlations in field interactions.

Findings

Bell-CHSH violation decreases due to field interaction

Exact density matrix derived via modular theory

Quantum field interaction reduces quantum nonlocality

Abstract

The interaction between Unruh-De Witt spin $1/2$ detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom. The resulting density matrix is employed to the study of the Bell-CHSH correlator. It turns out that, as a consequence of the interaction with the quantum field, the violation of the Bell-CHSH inequality exhibits a decreasing as compared to the case in which the scalar field is absent.