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  • Letter
  • Open Access

Maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality via bumpified Haar wavelets

David Dudal1,2, Philipe De Fabritiis3, Marcelo S. Guimaraes4, Itzhak Roditi3, and Silvio P. Sorella4

  • 1KU Leuven Campus Kortrijk–Kulak, Department of Physics, Etienne Sabbelaan 53 bus 7657, 8500 Kortrijk, Belgium
  • 2Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000 Gent, Belgium
  • 3CBPF—Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil
  • 4UERJ—Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, Brazil

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Phys. Rev. D 108, L081701 – Published 9 October, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L081701

Abstract

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+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.

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Phys. Rev. D 108, L081701– Published 9 October, 2023
  • Received 13 July 2023
  • Accepted 18 September 2023
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