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arXiv quant-ph/0512153quant-ph
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贝尔不等式的渐近破坏与可解性

Asymptotic violation of Bell inequalities and distillability

Ll. Masanes

发表信息：
Phys. Rev. Lett. 97, 050503 (2006)
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摘要：

一个多体量子态渐近地违反了一个贝尔不等式，如果在用一般的局部操作联合处理它的任意大数量的副本之后，结果违反了该不等式。在二分的情况下，我们表明，渐近违反的CHSH-不等式是等价的可验证性。在多体情况下，我们考虑了每个点有两个二分观测量的全相关贝尔不等式，也称为WWZB-不等式。我们表明，渐近违反任何这些不等式的多体状态意味着纯态纠缠可以从它蒸馏，虽然相应的蒸馏协议可能需要一些缔约方加入到几个群体。我们还得到了由测量具有两个二分观测量的$N$量子系统产生的分布集的极值点。研究表明，当考虑预处理后任何贝尔不等式的违反时，确定性LOCC或随机局部操作（无通信）就足够了。

英文摘要：

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the CHSH-inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site, also called WWZB-inequalities. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring $N$ quantum systems with two dichotomic observables per site. It is shown that when considering the violation of any Bell inequality after preprocessing, either deterministic LOCC or stochastic local operations (without communication) is enough.

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