arXiv:2410.19101 · Reviews in Physics

Bell’s inequality in relativistic Quantum Field Theory

M. S. Guimarães, I. Roditi, Silvio Paolo sorella

Published May 6, 2025• 10 citations

Abstract

A concise and self-contained introduction to the Bell inequality in relativistic Quantum Field Theory is presented. Taking the example of a real scalar massive field, the violation of the Bell inequality in the vacuum state and for causal complementary wedges is illustrated.

DOI: 10.1016/j.revip.2025.100121

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arXiv:2410.19101 · Reviews in Physics

Bell’s inequality in relativistic Quantum Field Theory

M. S. Guimarães, I. Roditi, Silvio Paolo sorella

Published May 6, 2025• 10 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.revip.2025.100121

Related papers

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A cat state localized in the right Rindler wedge is employed to study the violation of the Bell-CHSH inequality in a relativistic scalar free Quantum Field Theory. By means of the bounded Hermitian operator $sign(\varphi(f))$ , where $\varphi(f)$ stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.A cat state localized in the right Rindler wedge is employed to study the violation of the Bell-CHSH inequality in a relativistic scalar free Quantum Field Theory. By means of the bounded Hermitian operator $sign(\varphi(f))$, where $\varphi(f)$ stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.

hep-thCross-listedarXiv:2601.05216Physical review. D/Physical review. D.Jan 9, 20261 citation

The Bell-CHSH inequality in the vacuum state of a relativistic scalar quantum field is revisited by making use of the Hilbert space

{\cal H} \otimes {\cal H}_{AB}

, where

{\cal H}

and

{\cal H}_{AB}

stand, respectively, for the Hilbert space of the scalar field and of a generic bipartite quantum mechanical system. The construction of Hermitian, field-dependent, dichotomic operators is devised as well as the Bell-CHSH inequality. Working out the

AB

part of the inequality, the resulting Bell-CHSH correlation function for the quantum field naturally emerges from unitary Weyl operators. Furthermore, introducing a Jaynes-Cummings type Hamiltonian accounting for the interaction between the scalar field and a pair of qubits, the quantum corrections to the Bell-CHSH inequality in the vacuum state of the scalar field are evaluated till the second order in perturbation theory.

sign(\varphi(f))

, where

\varphi(f)

stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.