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Introduction to Bell's inequality in Quantum Mechanics

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arxiv 2409.07597 v3 pith:4SSH2HNE submitted 2024-09-11 quant-ph hep-thmath-phmath.MP

classification quant-phhep-thmath-phmath.MP
keywords bellinequalityintroductionmechanicsquantumstatescoherentexamples
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abstract

A pedagogical introduction to Bell's inequality in Quantum Mechanics is presented. Several examples, ranging from spin $1/2$ to coherent and squeezed states are worked out. The generalization to Mermin's inequalities and to GHZ states is also outlined.

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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. 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.

  3. Entangled Schr\"odinger cat states, vacuum projector and Bell-CHSH inequality

    quant-ph 2025-01 reject novelty 4.0 of 10

    A proposed vacuum-projector-based Bell test for Schrödinger cat states claims large Bell-CHSH violations, but the chosen equal measurement settings reduce the test to a single correlation bounded by 2.

  4. Bell and Mermin inequalities in Quantum Field Theory from vacuum projectors and Weyl operators

    quant-ph 2025-01 conditional novelty 4.0 of 10

    Bell-CHSH and Mermin inequalities are numerically violated in a 1+1 scalar field theory using vacuum-projector and Weyl operators, with violations increasing toward the Tsirelson bound as mass decreases.

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