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

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arxiv 2307.04611 v3 pith:B26RHVHO submitted 2023-07-10 hep-th quant-ph

David Dudal , Philipe De Fabritiis , Marcelo S. Guimaraes , Itzhak Roditi , Silvio P. Sorella This is my paper · ORCID
classification hep-thquant-ph
keywords testbell-chshfunctionsinequalityalicebumpifiedfieldhaar
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abstract

We devise a general setup to investigate the violation of the 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 to scrutinize Bell-CHSH inequalities with generic, interacting Quantum Field Theories.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modular wedge localization, Majorana fields and the Tsirelson limit of the Bell-CHSH inequality

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    In the massive Majorana field in 1+1 dimensions, the vacuum Bell-CHSH correlator is reduced to a single spectral weight, with the Tsirelson bound approached as the weight concentrates near modular eigenvalue 1.

  2. On a class of bounded Hermitian operators for the Bell-CHSH inequality in Quantum Field Theory

    quant-ph 2025-05 conditional novelty 6.0 of 10

    Explicit bounded Hermitian operators built from Weyl operators violate the Bell-CHSH inequality in the vacuum of a 1+1 scalar QFT, with a numerical construction matching modular-theory predictions.

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

    hep-th 2026-03 conditional novelty 5.0 of 10

    Modular operators construct wedge-localized one-particle vectors that produce Bell-CHSH violations ~2.3 for free scalar fields, with an outline for approaching Tsirelson's bound via modular-spectrum-aware operators.

  4. More on Majorana fields, modular localization and near saturation of the Tsirelson bound

    hep-th 2026-07 unverdicted novelty 4.5 of 10

    Modular wedge localization of free massless Majorana fields in 1+1 dimensions yields Bell-CHSH correlators that approach the Tsirelson bound of 2√2.

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