arXiv:2506.00504

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

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

Published May 31, 2025• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.2506.00504

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arXiv:2506.00504

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

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

Published May 31, 2025• 0 citations

arXiv HTML PDF

Abstract

1+1

Minkowski spacetime is scrutinized.

DOI: 10.48550/arxiv.2506.00504

Related papers

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.

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arXiv:2411.03485Nov 5, 20240 citations

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

1+1

Minkowski spacetime is scrutinized.

1+1

Minkowski spacetime is scrutinized.

Abstract Unitary transformations are employed to enhance the violations of the Bell-CHSH inequality in relativistic quantum field theory. The case of the scalar field in

1+1

1 + 1 Minkowski space-time is scrutinized by relying on the Tomita–Takesaki modular theory. The example of the bounded Hermitian operator

sign(\varphi (f))

s i g n ( φ ( f ) ) , where

\varphi (f)

φ ( f ) stands for the smeared scalar field, is worked out. It is shown that unitary deformations enable for violations of the Bell-CHSH inequality. The setup is generalized to the Proca vector field by means of its equivalence with the scalar theory.

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.

1+1

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.

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.

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.