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arXiv quant-ph/9910122quant-ph
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二阶二分束缚纠缠态不存在

Rank Two Bipartite Bound Entangled States Do Not Exist

Pawel Horodecki, John A. Smolin, Barbara M. Terhal, Ashish V. Thapliyal

摘要:

研究了二分密度矩阵的秩与束缚纠缠的关系。我们显示的秩,边际秩,和可扩展性的混合状态之间的关系,并使用此证明任何秩n束缚纠缠态必须有支持不超过n \times n希尔伯特空间。这个结果的一个直接结果是,不存在秩为2的两体束缚纠缠态。我们还证明了一个量子熵不等式形式的可分性条件与上述结果相关联。我们探讨了在混合物中需要多少个纯态才能消除Schmidt秩为n的纯态的纠缠,并给出了n-1的下界。我们还证明了非零量的任意纯纠缠态与纯乘积态的混合是可量子化的。

英文摘要:

We explore the relation between the rank of a bipartite density matrix and the existence of bound entanglement. We show a relation between the rank, marginal ranks, and distillability of a mixed state and use this to prove that any rank n bound entangled state must have support on no more than an n \times n Hilbert space. A direct consequence of this result is that there are no bipartite bound entangled states of rank two. We also show that a separability condition in terms of a quantum entropy inequality is associated with the above results. We explore the idea of how many pure states are needed in a mixture to cancel the distillable entanglement of a Schmidt rank n pure state and provide a lower bound of n-1. We also prove that a mixture of a non-zero amount of any pure entangled state with a pure product state is distillable.

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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