Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory

TL;DR

This paper uses modular theory and wedge localization in relativistic quantum field theory to analyze potential violations of the Bell-CHSH inequality and explore conditions for reaching Tsirelson's bound.

Contribution

It introduces a novel construction of wedge localized vectors in 1+1 dimensional scalar fields to study Bell inequality violations in a relativistic setting.

Findings

Constructed wedge localized vectors in 1+1D scalar QFT.

Analyzed Bell-CHSH inequality violations using Weyl and other operators.

Outlined a pathway towards saturating Tsirelson's bound.

Abstract

The Tomita-Takesaki modular theory is employed to discuss the Bell-CHSH inequality in wedge regions. By using the Bisognano-Wichmann results, the construction of a set of wedge localized vectors in the one-particle Hilbert space of a relativistic massive scalar field in $1+1$ dimensions is devised to establish whether violations of the Bell-CHSH inequality might occur for different choices of Bell's operators. In particular, the construction of the wedge localized vectors employed in the seminal work by Summers-Werner is scrutinized and applied to Weyl and other operators. We also outline a possible path towards the saturation of Tsirelson's bound.