Hypercontractivity for Semigroups of Unital Qubit Channels
Hypercontractivity for Semigroups of Unital Qubit Channels
复制标题
单位量子位通道半群的超收缩性
DOI：
10.1007/s00220-014-1982-4
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发表时间：
2012
影响因子：
2.4
通讯作者：
C. King
中科院分区：
文献类型：
--
作者：
C. King
证明了属于自伴半群的量子比特通道的乘积的超压缩性。超压缩界给出了形式为$${e^{-t_1 H_1}\otimes \cdots \otimes e^{- t_n H_n}}$$e-t1 H1的乘积是Lp到Lq的压缩的充要条件，其中Lp是具有归一化Schatten范数的2n维矩阵的代数，每个生成元Hj是二维矩阵代数上的自伴半正定算子。作为一个特殊的情况下，该结果建立了量子比特去极化通道的乘积的超压缩界。
Hypercontractivity is proved for products of qubit channels that belong to self-adjoint semigroups. The hypercontractive bound gives necessary and sufficient conditions for a product of the form $${e^{-t_1 H_1}\otimes \cdots \otimes e^{- t_n H_n}}$$e-t1H1⊗⋯⊗e-tnHn to be a contraction from Lp to Lq, where Lp is the algebra of 2n-dimensional matrices equipped with the normalized Schatten norm, and each generator Hj is a self-adjoint positive semidefinite operator on the algebra of 2-dimensional matrices. As a particular case the result establishes the hypercontractive bound for a product of qubit depolarizing channels.
影响因子：
1.3
作者：
Montanaro A
通讯作者：
Montanaro A