Bernards Fabian, Gühne Otfried
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany.
Phys Rev Lett. 2020 Nov 13;125(20):200401. doi: 10.1103/PhysRevLett.125.200401.
Bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing. Identifying inequalities for many particles or measurements is, however, difficult due to the computational complexity of characterizing the set of local correlations. We develop a method to characterize Bell inequalities under constraints, which may be given by symmetry or other linear conditions. This allows one to search systematically for generalizations of given Bell inequalities to more parties. As an example, we find all possible generalizations of the two-particle inequality by Froissart [Nuovo Cimento Soc. Ital. Fis. B 64, 241 (1981)], also known as I3322 inequality, to three particles. For the simplest of these inequalities, we study their quantum mechanical properties and demonstrate that they are relevant, in the sense that they detect nonlocality of quantum states, for which all two-setting inequalities fail to do so.
贝尔不等式是研究非局域关联及其在量子信息处理中应用的核心工具。然而，由于刻画局部关联集的计算复杂性，识别多粒子或多测量的不等式是困难的。我们开发了一种在约束条件下刻画贝尔不等式的方法，这些约束条件可以由对称性或其他线性条件给出。这使得人们能够系统地搜索给定贝尔不等式到更多参与方的推广。例如，我们找到了弗罗萨尔[《意大利新物理学报B》64, 241 (1981)]给出的两粒子不等式（也称为I3322不等式）到三粒子的所有可能推广。对于这些不等式中最简单的那些，我们研究了它们的量子力学性质，并证明它们是相关的，即它们能检测量子态的非局域性，而所有双设置不等式都无法做到这一点。
