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.

我们在证明助理 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，包括密度矩阵和射影测量，以及爱因斯坦提倡的用于模拟量子力学的局部隐变量假设无法成立的证明。后一个结果的证明基于所谓的 CHSH 不等式，而 Aspect 则通过实验证明了对这种不等式的违反，他因其工作而获得了 2022 年诺贝尔奖。我们还形式化了与违反 CHSH 不等式相关的各种结果，例如 Tsirelson 界限，它量化了在量子环境中可以违反这种不等式的程度。