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arXiv quant-ph/0503070quant-ph
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量子信道容量的简易测试

Simple test for quantum channel capacity

Pawel Horodecki, Marcin L. Nowakowski

摘要:

基于态同构和信道同构,指出半定规划可以作为非零单向量子信道容量的快速测试方法。这可以通过搜索同构于给定量子信道的状态的对称扩展来实现。利用这种方法,我们提供了量子信道的例子,可以导致高纠缠传输,但仍然有零的单向容量,特别是,区域的对称可扩展性的各向同性态在任意尺寸。此外,我们推导出{ \it一个新的纠缠参数}的基础上(归一化)的相对熵距离的一组状态,具有对称的扩展和明确显示的对称扩展的各向同性的状态是最接近的单态的对称扩展的状态。适当的正则化参数提供了一个新的上限单向可压缩纠缠。

英文摘要:

Basing on states and channels isomorphism we point out that semidefinite programming can be used as a quick test for nonzero one-way quantum channel capacity. This can be achieved by search of symmetric extensions of states isomorphic to a given quantum channel. With this method we provide examples of quantum channels that can lead to high entanglement transmission but still have zero one-way capacity, in particular, regions of symmetric extendibility for isotropic states in arbitrary dimensions are presented. Further we derive {\it a new entanglement parameter} based on (normalised) relative entropy distance to the set of states that have symmetric extensions and show explicitly the symmetric extension of isotropic states being the nearest to singlets in the set of symmetrically extendible states. The suitable regularisation of the parameter provides a new upper bound on one-way distillable entanglement.

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