Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2401.03313 · Journal of High Energy Physics

Unruh-De Witt detectors, Bell-CHSH inequality and Tomita-Takesaki theory

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

Published Jun 6, 2024• 7 citations
arXivHTMLPDF

Abstract

A bstract The interaction between Unruh-De Witt spin 1/2 detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom. The resulting density matrix is employed to the study of the Bell-CHSH correlator. It turns out that, as a consequence of the interaction with the quantum field, the violation of the Bell-CHSH inequality exhibits a decreasing as compared to the case in which the scalar field is absent.

DOI
10.1007/jhep06(2024)031

Related papers

A Study of Spin 1 Unruh–De Witt Detectors

F. M. Guedes, M. S. Guimarães, I. Roditi +1 more

A study of the interaction of spin 1 Unruh–De Witt detectors with a relativistic scalar quantum field is presented here. After tracing out the field modes, the resulting density matrix for a bipartite qutrit system is employed to investigate the violation of the Bell–CHSH inequality. Unlike the case of spin 1/2, for which the effects of the quantum field result in a decrease in the size of violation, in the case of spin 1, both a decrease or an increase in the size of the violation may occur. This effect is ascribed to the fact that Tsirelson’s bound is not saturated in the case of qutrits.

arXiv:2406.04362•Universe•Jul 24, 2024•1 citation

Tomita-Takesaki theory and quantum concurrence

Rupak Chatterjee

The quantum entanglement measure of concurrence is shown to be directly calculable from a Tomita- Takesaki modular operator framework constructed from the local von Neumann algebras of observables for two quantum systems. Specifically, the Tomita-Takesaki modular conjugation operator $J$ that links two separate systems with respect to their von Neumann algebras is related to the quantum concurrence $C$ of a pure bivariate entangled state composed from these systems. This concurrence relation provides a direct physical meaning to $J$ as both a symmetry operator and a quantitative measure of entanglement. This procedure is then demonstrated for a supersymmetric quantum mechanical system and a real scalar field interacting with two entangled spin-$\frac{1}{2}$ Unruh-DeWitt qubit detectors. For the latter system, the concurrence result is shown to be consistent with some known results on the Bell-CHSH inequality for such a system.

arXiv:2406.15900•Physical review. D/Physical review. D.•Sep 16, 2024•5 citations

Modular Theory and the Bell-CHSH inequality in relativistic scalar Quantum Field Theory

J. G. A. Caribé, M. S. Guimaraes, I. Roditi +1 more

The Tomita-Takesaki modular theory is employed to discuss the Bell-CHSH inequality in wedge regions. By using the Bisognano-Wichmann results, the construction of a set of wedge localized vectors in the one-particle Hilbert space of a relativistic massive scalar field in $1+1$ 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.

hep-thCross-listedarXiv:2603.25873•Mar 30, 2026•0 citations

Modular theory and the Bell-CHSH inequality in relativistic scalar quantum field theory

J. G. A. Caribé, M. S. Guimarães, I. Roditi +1 more

Abstract The Tomita–Takesaki modular theory is employed to discuss the Bell-CHSH inequality in wedge regions. By using the Bisognano–Wichmann results, the construction of a set of wedge localized vectors in the one-particle Hilbert space of a relativistic massive scalar field in $$1+1$$ 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.

The European Physical Journal C•Jul 18, 2026•0 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.

arXiv:2506.00504•May 31, 2025•0 citations

Bell-CHSH inequality and unitary transformations in quantum field theory

D. O. R. Azevedo, F. M. Guedes, M. S. Guimarães +3 more

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.

arXiv:2412.03840•The European Physical Journal C•Mar 6, 2026•0 citations
A bstract The interaction between Unruh-De Witt spin 1/2 detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom. The resulting density matrix is employed to the study of the Bell-CHSH correlator. It turns out that, as a consequence of the interaction with the quantum field, the violation of the Bell-CHSH inequality exhibits a decreasing as compared to the case in which the scalar field is absent.
A study of the interaction of spin 1 Unruh–De Witt detectors with a relativistic scalar quantum field is presented here. After tracing out the field modes, the resulting density matrix for a bipartite qutrit system is employed to investigate the violation of the Bell–CHSH inequality. Unlike the case of spin 1/2, for which the effects of the quantum field result in a decrease in the size of violation, in the case of spin 1, both a decrease or an increase in the size of the violation may occur. This effect is ascribed to the fact that Tsirelson’s bound is not saturated in the case of qutrits.
The quantum entanglement measure of concurrence is shown to be directly calculable from a Tomita- Takesaki modular operator framework constructed from the local von Neumann algebras of observables for two quantum systems. Specifically, the Tomita-Takesaki modular conjugation operator JJJ that links two separate systems with respect to their von Neumann algebras is related to the quantum concurrence CCC of a pure bivariate entangled state composed from these systems. This concurrence relation provides a direct physical meaning to JJJ as both a symmetry operator and a quantitative measure of entanglement. This procedure is then demonstrated for a supersymmetric quantum mechanical system and a real scalar field interacting with two entangled spin-12\frac{1}{2}21​ Unruh-DeWitt qubit detectors. For the latter system, the concurrence result is shown to be consistent with some known results on the Bell-CHSH inequality for such a system.
The Tomita-Takesaki modular theory is employed to discuss the Bell-CHSH inequality in wedge regions. By using the Bisognano-Wichmann results, the construction of a set of wedge localized vectors in the one-particle Hilbert space of a relativistic massive scalar field in 1+11+11+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.
Abstract The Tomita–Takesaki modular theory is employed to discuss the Bell-CHSH inequality in wedge regions. By using the Bisognano–Wichmann results, the construction of a set of wedge localized vectors in the one-particle Hilbert space of a relativistic massive scalar field in 1+11+11+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.
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+11+11+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+11+11+1 1 + 1 Minkowski space-time is scrutinized by relying on the Tomita–Takesaki modular theory. The example of the bounded Hermitian operator sign(φ(f))sign(\varphi (f))sign(φ(f)) s i g n ( φ ( f ) ) , where φ(f)\varphi (f)φ(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.