A Formalization of the CHSH Inequality and Tsirelson’s Upper-bound in Isabelle/HOL - Systèmes intelligents pour les données, les connaissances et les humains
Article Dans Une Revue Journal of Automated Reasoning Année : 2023

A Formalization of the CHSH Inequality and Tsirelson’s Upper-bound in Isabelle/HOL

Mnacho Echenim
Mehdi Mhalla

Résumé

We present a formalization of several fundamental notions and results from Quantum Information theory in the proof assistant Isabelle/HOL, including density matrices and projective measurements, along with the proof that the local hidden-variable hypothesis advocated by Einstein to model quantum mechanics cannot hold. The proof of the latter result is based on the so-called CHSH inequality, and it is the violation of this inequality that was experimentally evidenced by Aspect, who earned the Nobel Prize in 2022 for his work. We also formalize various results related to the violation of the CHSH inequality, such as Tsirelson’s bound, which quantifies the amount to which this inequality can be violated in a quantum setting.
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Dates et versions

hal-04740770 , version 1 (07-01-2025)

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Mnacho Echenim, Mehdi Mhalla. A Formalization of the CHSH Inequality and Tsirelson’s Upper-bound in Isabelle/HOL. Journal of Automated Reasoning, 2023, 68 (1), pp.2. ⟨10.1007/s10817-023-09689-9⟩. ⟨hal-04740770⟩
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