Bell-CHSH inequality and unitary transformations in Quantum Field Theory

TL;DR

This paper investigates how unitary transformations can enhance Bell-CHSH inequality violations in relativistic Quantum Field Theory, using modular theory and specific operators in scalar and vector fields.

Contribution

It demonstrates that unitary deformations can increase Bell-CHSH violations and generalizes the approach from scalar to Proca vector fields.

Findings

Unitary transformations can enhance Bell-CHSH violations.

The scalar field example confirms the effectiveness of deformations.

The method extends to Proca vector fields.

Abstract

Unitary transformations are employed to enhance the violations of the Bell-CHSH inequality in relativistic Quantum Field Theory. The case of the scalar field in $1+1$ Minkowski space-time is scrutinized by relying on the Tomita-Takesaki modular theory. The example of the bounded Hermitian operator $sign(\varphi(f))$, where $\varphi(f)$ stands for the smeared scalar field, is worked out. It is shown that unitary deformations enable for violations of the Bell-CHSH inequality. The setup is generalized to the Proca vector field by means of its equivalence with the scalar theory.