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Cat states and violation of the Bell-Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory

M. S. Guimaraes1,*, I. Roditi2,†, and S. P. Sorella1,‡

  • *Contact author: msguimaraes@uerj.br
  • †Contact author: roditi@cbpf.br
  • ‡Contact author: silvio.sorella@fis.uerj.br
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Phys. Rev. D 113, 065008 – Published 13 March, 2026

DOI: https://doi.org/10.1103/bgxv-pcjx

Abstract

A cat state localized in the right Rindler wedge is employed to study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality in a relativistic scalar-free quantum field theory. By means of the bounded Hermitian operator sign(φ(f)), where φ(f) stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms, which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.

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Phys. Rev. D 113, 065008– Published 13 March, 2026
  • Received 11 January 2026
  • Accepted 19 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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