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

Abstract

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.

8 pages, 3 figures. Final version, to appear in JHEP

References in corpus (4)

• Weyl operators, Tomita-Takesaki theory, and Bell-Clauser-Horne-Shimony-Holt inequality violations
• Entanglement and maximal violation of the CHSH inequality in a system of two spins j: a novel construction and further observations
• Non-perturbative simple-generated interactions with a quantum field for arbitrary Gaussian states
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Cited by in corpus (6)

• Imprints of screened dark energy on nonlocal quantum correlations
• Numerical approach to the Bell-Clauser-Horne-Shimony-Holt inequality in quantum field theory
• Tomita-Takesaki theory and quantum concurrence
• Harvesting Contextuality from the Vacuum
• A study of the spin 1 Unruh-De Witt detectors
• Harvesting stabilizer entropy and non-locality from a quantum field