Two-party Bell inequalities derived from combinatorics via triangular elimination
Two-party Bell inequalities derived from combinatorics via triangular elimination
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DOI：
10.1088/0305-4470/38/50/007
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发表时间：
2005-05
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影响因子：
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通讯作者：
D. Avis;H. Imai;Tsuyoshi Ito;Yuuya Sasaki
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文献类型：
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作者：
D. Avis;H. Imai;Tsuyoshi Ito;Yuuya Sasaki
本文建立了二值测量的两方Bell不等式与多面体组合学中称为截多面体的高维凸多面体之间的关系。利用这种关系，我们提出了一种方法，三角消除，得到紧贝尔不等式切割多面体的方面。该方法从割多面体的已有结果出发，给出了2亿个不等价的紧Bell不等式.此外，该方法还给出了表示无穷多个Bell不等式族的一般公式。这些结果可用于检验Bell不等式的一般性质.
We establish a relation between the two-party Bell inequalities for two-valued measurements and a high-dimensional convex polytope called the cut polytope in polyhedral combinatorics. Using this relation, we propose a method, triangular elimination, to derive tight Bell inequalities from facets of the cut polytope. This method gives two hundred million inequivalent tight Bell inequalities from currently known results on the cut polytope. In addition, this method gives general formulae which represent families of infinitely many Bell inequalities. These results can be used to examine general properties of Bell inequalities.