On the relationship between convex bodies related to correlation experiments with dichotomic observables
On the relationship between convex bodies related to correlation experiments with dichotomic observables
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DOI：
10.1088/0305-4470/39/36/010
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发表时间：
2006-05
期刊：
影响因子：
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通讯作者：
D. Avis;H. Imai;Tsuyoshi Ito McGill University;T. U. O. Tokyo;Japan Science;Technology Agency;Japan Science
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文献类型：
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作者：
D. Avis;H. Imai;Tsuyoshi Ito McGill University;T. U. O. Tokyo;Japan Science;Technology Agency;Japan Science
在本文中，我们进一步探讨凸体与二分变量的量子相关实验和相关机构的组合优化研究，特别是切割多面体之间的联系。在Avis等人（2005 J.Phys.A：Math.Gen.38 10971-87）中关于Bell不等式建立了这种关系。我们发现，几个著名的机构有关的切割多面体是等价的机构，如定义的Tsirelson（1993年强子J。增刊8 329-45），以代表隐藏的确定性行为，量子行为和无信号行为。除此之外，我们的结果允许这些机构的一个独特的表示，给顶点的无信号多面体的必要条件，并给出了一种方法，通过一个机构，包含一套量子行为的约束量子违反贝尔不等式。优化后一机构可以有效地执行半定规划。在本文的第二部分中，我们将这些结果应用于经典相关函数的研究。当m = 4，n = 4和min{m，n} ≤ 3时，我们给出了（m，n）二分观测量的两方情形的一个完整的紧不等式列表，并给出了一个新的广义相关不等式族.
In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis et al (2005 J. Phys. A: Math. Gen. 38 10971–87) with respect to Bell inequalities. We show that several well-known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. Suppl. 8 329–45) to represent hidden deterministic behaviours, quantum behaviours and no-signalling behaviours. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviours. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m, n) dichotomic observables when m = 4, n = 4 and when min{m, n} ≤ 3, and give a new general family of correlation inequalities.