德国马克斯·普朗克光科学研究所Andrea Aiello研究组探明了贝尔定理的无不等式证明。这一研究成果发表在2025年3月4日出版的《物理评论A》上。

贝尔定理被认为证明了量子力学和局部现实隐变量理论之间不可调和的冲突。贝尔定理的大多数证明都是基于不等式的。

研究组提出了一种不涉及不等式的替代证明，而只是将使用量子力学计算的相关函数与根据局部现实隐变量理论计算的关联函数进行直接比较。该证明基于傅里叶级数对周期函数的物理动机使用，并证实了局部现实隐变量理论与量子力学不相容。

附：英文原文

Title: Inequality-free proof of Bell's theorem

Author: Andrea Aiello

Issue&Volume: 2025/03/04

Abstract: Bell's theorem supposedly demonstrates an irreconcilable conflict between quantum mechanics and local realistic hidden-variable theories. Most proofs of Bell's theorem, are based on inequalities. In this paper we present an alternative proof which does not involve inequalities, but only a direct comparison between correlation functions calculated using quantum mechanics on the one hand, and those calculated according to local realistic hidden-variable theories on the other. Our proof is based on a physically motivated use of Fourier series for periodic functions, and confirms that local realistic hidden-variable theories are incompatible with quantum mechanics.

DOI: 10.1103/PhysRevA.111.032204

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.032204