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The European Physical Journal C

Investigation of the Bell-CHSH inequality in diamond regions

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

Published Mar 24, 2025• 4 citations
Publisher

Abstract

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.

DOI
10.1140/epjc/s10052-025-14058-4

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Abstract A numerical setup for the Bell-CHSH inequality for causal diamonds in 1+11+11+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.
A numerical setup for the Bell-CHSH inequality for causal diamonds in 1+11+11+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 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.
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+11+11+1 Minkowski spacetime is scrutinized.
The Bell-CHSH (Clauser-Horne-Shimony-Holt) inequality in the vacuum state of a relativistic scalar quantum field is analyzed. Using Weyl operators built with smeared fields localized in the Rindler wedges, the Bell-CHSH inequality is expressed in terms of the Lorentz invariant inner products of test functions. A numerical framework for these inner products is devised. Causality is also explicitly checked by a numerical evaluation of the Pauli-Jordan function. Violations of the Bell-CHSH inequality are reported for different values of the particle mass parameter. Published by the American Physical Society 2024
We devise a general setup to investigate the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality in the vacuum state in the context of quantum field theory. We test the method with massless spinor fields in (1+11+11+1)-dimensional Minkowski space-time. Alice's and Bob's test functions are explicitly constructed, first by employing Haar wavelets which are then bumpified into proper test functions via a smoothening procedure relying on the Planck-taper window function. Relativistic causality is implemented by requiring the support of Alice's and Bob's test functions to be located in the left and right Rindler wedges, respectively. Violations of the Bell-CHSH inequality as close as desired to Tsirelson's bound are reported. We briefly comment on the extra portal, compared to earlier works; this opens the opportunity to scrutinize Bell-CHSH inequalities with generic, interacting quantum field theories.