What question did this study set out to answer?

The aim is to correct errors in the teaching of the CHSH inequality related to specific quantum states.

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February 6, 2026Open Access

State-Dependent CHSH Inequality: A Common Pedagogical Omission with Reproducible Verification

Key Points

The aim is to correct errors in the teaching of the CHSH inequality related to specific quantum states.
Identified omissions in standard pedagogical practices for the CHSH inequality.
Tested angular configurations for different Bell states.
Provided reproducible Python code for verification of results.
Demonstrated that optimal angular configurations differ for each Bell state.
Found that applying standard CHSH terms to |Φ⁺⟩ yields incorrect results, emphasizing the need for state-specific approaches.

Abstract

We identify and correct a common pedagogical omission in the presentation of the CHSH inequality. The angular configuration 0, π/2, π/4, -π/4, historically optimal for the singlet state |Ψ⁻⟩, yields S=0 when applied to |Φ⁺⟩ using the standard CHSH form. We demonstrate that each Bell state requires specific angular configurations and CHSH formula variants. Reproducible Python verification code is included. This work serves as an educational resource highlighting the importance of state-specific context in quantum mechanics pedagogy.

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Cite This Study

Erick Francisco Perez Eugenio (Wed,) studied this question.

synapsesocial.com/papers/698586ad8f7c464f2300a6d0 https://doi.org/https://doi.org/10.5281/zenodo.18475905

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