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arXiv 1006.3032quant-ph
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利用无穷维量子系统求解I3322不等式的最大破坏

Maximal violation of the I3322 inequality using infinite dimensional quantum systems

K. F. Pál, T. Vértesi

摘要:

I3322不等式是除Clauser-Horne-Shimony-Holt(CHSH)不等式之外最简单的二部两结果贝尔不等式,它由每一方三个两结果测量组成。在CHSH不等式的情况下,最大量子破坏已经可以在局域二维量子系统中实现,然而,I3322不等式没有这样的证据。本文给出了一族测量算符和态,使我们能够在无限维希尔伯特空间中获得最大可能的量子值。此外,它是强调,我们的建设是最佳的意义上,测量有限维量子系统是不足以实现真正的量子最大值。我们还描述了一个有效的迭代算法,用于计算任意给定Hilbert空间维中任意两个结果的贝尔不等式的量子最大值。该算法在获得I3322不等式的结果中起到了关键作用,同时我们也应用该算法改进了我们以前关于几个二分两结果贝尔不等式的最大量子破坏的结果,其中每一方最多可以有五个设置.

英文摘要:

The I3322 inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems, however, there is no such evidence for the I3322 inequality. In this paper a family of measurement operators and states is given which enables us to attain the largest possible quantum value in an infinite dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite dimensional quantum systems is not enough to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role to obtain our results for the I3322 inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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