arXiv:2501.03186 · Nuclear Physics B

Bell and Mermin inequalities in Quantum Field Theory from vacuum projectors and Weyl operators

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

Published May 12, 2025• 2 citations

Abstract

The use of the vacuum projector | 0 〉〈 0 | and of the unitary Weyl operators enables us to construct a set of Hermitian dichotomic operators in relativistic scalar Quantum Field Theory in Minkowski spacetime. Employing test functions supported in diamond regions, both Bell and Mermin inequalities are studied by means of a numerical setup. In addition to reporting expressive violations of both inequalities, the cluster property is also checked.

DOI: 10.1016/j.nuclphysb.2025.116942

Related papers

On a class of bounded Hermitian operators for the Bell-CHSH inequality in Quantum Field Theory

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

arXiv:2506.00504May 31, 20250 citations

Mermin's inequalities in Quantum Field Theory

Philipe De Fabritiis, I. Roditi, Silvio Paolo sorella

A relativistic Quantum Field Theory framework is devised for Mermin's inequalities. By employing smeared Dirac spinor fields, we are able to introduce unitary operators which create, out of the Minkowski vacuum |0〉, GHZ-type states. In this way, we are able to obtain a relation between the expectation value of Mermin's operators in the vacuum and in the GHZ-type states. We show that Mermin's inequalities turn out to be maximally violated when evaluated on these states.

arXiv:2303.12195Physics Letters BSep 25, 20236 citations

Investigation of the Bell-CHSH inequality in diamond regions

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

arXiv:2411.03485Nov 5, 20240 citations

Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality

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

arXiv:2407.14636Jul 19, 20240 citations

Class of bounded Hermitian operators for the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory

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

Physical review. D/Physical review. D.Sep 24, 20254 citations

Entangled Schrödinger cat states, vacuum projector and Bell-CHSH inequality

Silvio Paolo sorella

Abstract Use of the vacuum projector and of the unitary displacement operators enables us to construct Hermitian dichotomic operators. These operators are employed to scrutinize the violation of the Bell-CHSH inequality for entangled coherent Schrödinger cat states.

arXiv:2501.03960Journal of Physics A Mathematical and TheoreticalMay 21, 20250 citations

arXiv:2501.03186 · Nuclear Physics B

Bell and Mermin inequalities in Quantum Field Theory from vacuum projectors and Weyl operators

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

Published May 12, 2025• 2 citations

arXiv HTML PDF

Abstract

DOI: 10.1016/j.nuclphysb.2025.116942

Related papers

On a class of bounded Hermitian operators for the Bell-CHSH inequality in Quantum Field Theory

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

The violation of the Bell-CHSH inequality in a relativistic scalar Quantum Field Theory is analysed by means of a set of bounded Hermitian operators constructed out of the unitary Weyl operators. These operators allow for both analytic and numerical approaches. While the former relies on the modular theory of Tomita-Takesaki, the latter is devised through an explicit construction of the test functions needed for the localization of the aforementioned operators. The case of causal tangent diamonds in $1+1$ Minkowski spacetime is scrutinized.The violation of the Bell-CHSH inequality in a relativistic scalar Quantum Field Theory is analysed by means of a set of bounded Hermitian operators constructed out of the unitary Weyl operators. These operators allow for both analytic and numerical approaches. While the former relies on the modular theory of Tomita-Takesaki, the latter is devised through an explicit construction of the test functions needed for the localization of the aforementioned operators. The case of causal tangent diamonds in $1+1$ Minkowski spacetime is scrutinized.

arXiv:2506.00504May 31, 20250 citations

Mermin's inequalities in Quantum Field Theory

Philipe De Fabritiis, I. Roditi, Silvio Paolo sorella

arXiv:2303.12195Physics Letters BSep 25, 20236 citations

Investigation of the Bell-CHSH inequality in diamond regions

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

A numerical setup for the Bell-CHSH inequality for causal diamonds in $1+1$ Minkowski spacetime is presented. Upon choosing a suitable set of test functions supported in the diamonds, sensible violations are reported for the correlation function of Weyl operators of a real scalar massive field in the vacuum state.A numerical setup for the Bell-CHSH inequality for causal diamonds in $1+1$ Minkowski spacetime is presented. Upon choosing a suitable set of test functions supported in the diamonds, sensible violations are reported for the correlation function of Weyl operators of a real scalar massive field in the vacuum state.

arXiv:2411.03485Nov 5, 20240 citations

Gluing together Quantum Field Theory and Quantum Mechanics: a look at the Bell-CHSH inequality

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

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.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.

arXiv:2407.14636Jul 19, 20240 citations

Class of bounded Hermitian operators for the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory

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

The violation of the Bell-Clauser-Horne-Shimony-Holt inequality in a relativistic scalar quantum field theory is analyzed by means of a set of bounded Hermitian operators constructed out of the unitary Weyl operators. These operators allow for both analytic and numerical approaches. While the former relies on the modular theory of Tomita-Takesaki, the latter is devised through an explicit construction of the test functions needed for the localization of the aforementioned operators. The case of causal tangent diamonds in $1+1$ Minkowski spacetime is scrutinized.The violation of the Bell-Clauser-Horne-Shimony-Holt inequality in a relativistic scalar quantum field theory is analyzed by means of a set of bounded Hermitian operators constructed out of the unitary Weyl operators. These operators allow for both analytic and numerical approaches. While the former relies on the modular theory of Tomita-Takesaki, the latter is devised through an explicit construction of the test functions needed for the localization of the aforementioned operators. The case of causal tangent diamonds in $1+1$ Minkowski spacetime is scrutinized.

Physical review. D/Physical review. D.Sep 24, 20254 citations

Entangled Schrödinger cat states, vacuum projector and Bell-CHSH inequality

Silvio Paolo sorella

arXiv:2501.03960Journal of Physics A Mathematical and TheoreticalMay 21, 20250 citations

1+1

Minkowski spacetime is scrutinized.

A numerical setup for the Bell-CHSH inequality for causal diamonds in

1+1

Minkowski spacetime is presented. Upon choosing a suitable set of test functions supported in the diamonds, sensible violations are reported for the correlation function of Weyl operators of a real scalar massive field in the vacuum state.

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.

1+1

Minkowski spacetime is scrutinized.