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arXiv 0802.1360quant-ph
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可降解量子信道的结构

The structure of degradable quantum channels

Toby S. Cubitt, Mary-Beth Ruskai, Graeme Smith

备注：
42 pages, 3 figures, Web and paper abstract differ; (v2 contains only minor typo corrections)
发表信息：
J. Math. Phys. 49, 102104 (2008)
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摘要：

可降解的量子信道是唯一已知其量子和私有经典容量的信道之一。因此，确定这些通道的结构是量子信息理论中一个紧迫的开放问题。我们给出了一个全面的审查是什么，目前已知的可降解量子信道的结构，包括一些新的结果，以及一些已知结果的替代证明。在量子比特的情况下，我们给出了所有二维输出的可降解通道的完整刻画，给出了具有两个Kraus算子的量子比特通道是可降解的或不可降解的新证明，并给出了不可降解的单位量子比特通道的完整描述和新证明.对于更高的输出维度，我们探索可降解通道的输出和环境维度（分别为$d_B$和$d_E$）之间的关系。对于几个广泛的类别的渠道，我们表明，他们可以建模的环境是“小”的意义上$d_E \leq d_B$。也许令人惊讶的是，我们还提出了“大”环境的可降解通道的例子，在这个意义上，最小尺寸$d_E > d_B$。实际上，可以有$d_E > \tfrac{1}{4} d_B^2$。在对角Kraus算子通道的情况下，我们描述的子类是纠缠破坏通道的补充。我们也得到了一些结果的渠道在凸壳共轭广义泡利矩阵。然而，一些悬而未决的问题仍然存在这些渠道和更普遍的情况下，随机酉信道。

英文摘要：

Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the structure of degradable quantum channels, including a number of new results as well as alternate proofs of some known results. In the case of qubits, we provide a complete characterization of all degradable channels with two dimensional output, give a new proof that a qubit channel with two Kraus operators is either degradable or anti-degradable and present a complete description of anti-degradable unital qubit channels with a new proof. For higher output dimensions we explore the relationship between the output and environment dimensions ($d_B$ and $d_E$ respectively) of degradable channels. For several broad classes of channels we show that they can be modeled with a environment that is "small" in the sense $d_E \leq d_B$. Perhaps surprisingly, we also present examples of degradable channels with ``large'' environments, in the sense that the minimal dimension $d_E > d_B$. Indeed, one can have $d_E > \tfrac{1}{4} d_B^2$. In the case of channels with diagonal Kraus operators, we describe the subclass which are complements of entanglement breaking channels. We also obtain a number of results for channels in the convex hull of conjugations with generalized Pauli matrices. However, a number of open questions remain about these channels and the more general case of random unitary channels.

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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