Bell-CHSH inequality and unitary operators

TL;DR

This paper explores how specific unitary operators influence the Bell-CHSH inequality, highlighting conditions where classical and quantum bounds remain unchanged, with applications to relativistic quantum field theory.

Contribution

It identifies a class of unitary operators with real expectation values that do not alter the Bell-CHSH bounds, providing insights into their role in quantum violations.

Findings

Certain unitary operators preserve Bell-CHSH bounds

Real expectation value operators maintain classical and quantum bounds

Application to Weyl operators in relativistic quantum field theory

Abstract

Unitary operators are employed to investigate the violation of the Bell-CHSH inequality. The ensuing modifications affecting both classical and quantum bounds are elucidated. The relevance of a particular class of unitary operators whose expectation values are real is pointed out. For these operators, the classical and quantum bounds remain unaltered, being given, respectively, by $2$ and $2\sqrt{2}$. As an example, the Weyl unitary operators for a real scalar field in relativistic Quantum Field Theory are discussed.