arXiv:2411.03485

Investigation of the Bell-CHSH inequality in diamond regions

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

Published Nov 5, 2024• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.2411.03485

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arXiv:2411.03485

Investigation of the Bell-CHSH inequality in diamond regions

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

Published Nov 5, 2024• 0 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.48550/arxiv.2411.03485

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Investigation of the Bell-CHSH inequality in diamond regions

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

Abstract A numerical setup for the Bell-CHSH inequality for causal diamonds in $1+1$ 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.Abstract A numerical setup for the Bell-CHSH inequality for causal diamonds in $$1+1$$ 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 European Physical Journal CMar 24, 20254 citations

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.

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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

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

1+1

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

1+1

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.

1+1

Minkowski spacetime is scrutinized.

1+1

Minkowski spacetime is scrutinized.

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.