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

IF 0.9 3区计算机科学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Journal of Automated Reasoning Pub Date : 2023-12-19 DOI:10.1007/s10817-023-09689-9

引用次数: 0

Abstract

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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Isabelle/HOL 中 CHSH 不等式和齐雷尔森上界的形式化

摘要我们在证明助手 Isabelle/HOL 中提出了量子信息论的几个基本概念和结果的形式化，包括密度矩阵和投影测量，以及爱因斯坦提倡的量子力学模型的局部隐变量假设不成立的证明。后一个结果的证明基于所谓的 CHSH 不等式，而阿斯佩特正是通过实验证明了对这一不等式的违反，他也因此获得了 2022 年的诺贝尔奖。我们还形式化了与违反 CHSH 不等式有关的各种结果，例如齐雷尔森约束，它量化了在量子环境中违反该不等式的程度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Automated Reasoning 工程技术-计算机：人工智能

CiteScore

3.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning. The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.