arXiv 0810.16152008-10quant-ph

贝尔不等式的量子界

Quantum Bounds on Bell inequalities

K. F. Pál, T. Vértesi

备注：: 12 pages, 4 tables; corrected Table I and modified Table III to comply with Table I; more detailed results are available at http://www.atomki.hu/atomki/TheorPhys/Bell_violation/
发表信息：: Phys. Rev. A 79, 022120 (2009)
DOI：: 10.1103/PhysRevA.79.022120

摘要：

通过在六维复希尔伯特空间和八维实分量希尔伯特空间中构造相应的测量算子，我们确定了241个紧二分贝尔不等式的最大量子违反，其中每一方最多可有五个两结果测量设置.在这些不平等中，这里介绍了129个。在43种情况下，高维分量空间比量子位产生更大的违反，在3种情况下，最大值是在六维空间中实现的。我们还利用最近提出的一种方法计算了这些贝尔不等式的上界。除了20个不等式外，所有的最佳解都与上界相匹配。令人惊讶的是，最简单的不等式的设置检查，只有三个测量设置每一方，是不是其中，尽管考虑的希尔伯特空间的高维性。我们还计算了最大纠缠量子比特对的检测阈值效率。如果还允许简并测量，则在几种情况下可以降低这些。

英文摘要：

We have determined the maximum quantum violation of 241 tight bipartite Bell inequalities with up to five two-outcome measurement settings per party by constructing the appropriate measurement operators in up to six-dimensional complex and eight-dimensional real component Hilbert spaces using numerical optimization. Out of these inequalities 129 has been introduced here. In 43 cases higher dimensional component spaces gave larger violation than qubits, and in 3 occasions the maximum was achieved with six-dimensional spaces. We have also calculated upper bounds on these Bell inequalities using a method proposed recently. For all but 20 inequalities the best solution found matched the upper bound. Surprisingly, the simplest inequality of the set examined, with only three measurement settings per party, was not among them, despite the high dimensionality of the Hilbert space considered. We also computed detection threshold efficiencies for the maximally entangled qubit pair. These could be lowered in several instances if degenerate measurements were also allowed.

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