Bell inequalities from group actions of single-generator groups
Bell inequalities from group actions of single-generator groups
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DOI：
10.1103/physreva.90.062121
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
V. U. Guney;M. Hillery
中科院分区：
文献类型：
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作者：
V. U. Guney;M. Hillery
研究了利用单生成元交换群的群作用生成Bell不等式的方法。两方，Alice和Bob，各自对系统进行M个可能的测量之一，每个测量有K个可能的结果。这些测量结果的概率为P（a_j = k，B_{j '}= k'），其中j，j'在集合{1，2，. M}和k，k'在集合{0，1，. K-1}。当这些概率来自于一个局部的、现实的理论时，这些概率的某些子集的和有上限，而如果这些概率来自于量子力学，那么这些概率就可能被违反。在我们的例子中，概率的子集是由一个群作用产生的，特别是，一个单生成元群在张量积希尔伯特空间中作用于乘积态的表示。我们展示了这在几种情况下是如何工作的，包括M=2，K=3和一般的M，K=2。我们还讨论了由此产生的不平等的非局部游戏。
We study a method of generating Bell inequalities by using group actions of single-generator abelian groups. Two parties, Alice and Bob, each make one of M possible measurements on a system, with each measurement having K possible outcomes. The probabilities for the outcomes of these measurements are P(a_j = k, b_{j'}=k'), where j,j' are in the set {1,2,... M} and k,k' are in the set {0,1,... K-1}. The sums of some subsets of these probabilities have upper bounds when the probabilities result from a local, realistic theory that can be violated if the probabilities come from quantum mechanics. In our case the subsets of probabilities are generated by a group action, in particular, a representation of a single-generator group acting on product states in a tensor-product Hilbert space. We show how this works for several cases, including M=2, K=3, and general M, K=2. We also discuss the resulting inequalities in terms of nonlocal games.