arXiv quant-ph/03041762003-04-28quant-ph

作为非局部相关通信代价下界的贝尔不等式违反

Violations of Bell inequalities as lower bounds on the communication cost of non-local correlations

Stefano Pironio

备注：: 9 pages, revtex
发表信息：: Phys. Rev. A 68, 062102 (2003)
DOI：: 10.1103/PhysRevA.68.062102

摘要：

为了在局部隐变量理论中重现违反贝尔不等式的相关性，各方之间必须进行通信。我们发现，违反贝尔不等式的金额施加了一个下界的平均通信需要产生这些相关性。此外，对于每一个概率分布，存在一个最优不等式，使违反的程度给出最小的平均通信。例如，为了使用经典资源产生最大程度违反CHSH不等式的相关性，0.4142比特的通信是必要的和足够的。对于在两个d>=3的纠缠态上进行的Bell测试，其中每一方都可以在两个测量之间进行选择，我们的结果表明，与最大纠缠态相比，需要更多的通信来模拟从某些非最大纠缠态获得的结果。

英文摘要：

To reproduce in a local hidden variables theory correlations that violate Bell inequalities, communication must occur between the parties. We show that the amount of violation of a Bell inequality imposes a lower bound on the average communication needed to produce these correlations. Moreover, for every probability distribution there exists an optimal inequality for which the degree of violation gives the minimal average communication. As an example, to produce using classical resources the correlations that maximally violate the CHSH inequality, 0.4142 bits of communication are necessary and sufficient. For Bell tests performed on two entangled states of dimension d>=3 where each party has the choice between two measurements, our results suggest that more communication is needed to simulate outcomes obtained from certain non-maximally entangled states than maximally entangled ones.

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