A Quantum Representation for Involution Groups
A Quantum Representation for Involution Groups
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合合群的量子表示
DOI：
10.1016/j.entcs.2011.09.019
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
T. Crowder
中科院分区：
文献类型：
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作者：
T. Crowder
我们回答 Martin 等人提出的问题。在 MFPS XXVI 中得到肯定：有限对合群上的自由仿射幺半群除了 [Martin, K., J. Feng, 和 S. Krishnan. 中已经证明存在的经典表示之外，还具有量子表示。量子信息论中的自由对象。理论计算机科学电子笔记 267 (2010), 35–47]。特别是，这意味着在每个维度中都存在非平凡的量子通道类别，它们具有低维度中不存在的经典表示。在建立这一结果的过程中，我们给出了对角 n 量子位通道的两个特征（其中之一在 [Bourdon, P.S, and H.T. Williams, UnitalQuantum Operations on the Bloch ball and Bloch Region, Phys. Rev. A. 69 (2004), 022314] 中所述）以及 Bloch 矩阵满足的必要条件。
We answer a question posed by Martin et al. at MFPS XXVI in the affirmative: the free affine monoid over a finite involution group has a quantum representation, in addition to the classical representation already shown to exist in [Martin, K., J. Feng, and S. Krishnan. A Free Object in Quantum Information Theory. Electronic Notes in Theoretical Computer Science 267 (2010), 35–47]. In particular, this implies that in every dimension there are non-trivial classes of quantum channels that have classical representations which were not present in the lower dimensions. En route to establishing this result, we give two characterizations of the diagonal n-qubit channels (one of which is stated in [Bourdon, P.S, and H.T. Williams, Unital quantum operations on the Bloch ball and Bloch region, Phys. Rev. A. 69 (2004), 022314]) and necessary conditions for a Bloch matrix to satisfy.