A fibre bundle over manifolds of quantum channels and its application to quantum statistics
A fibre bundle over manifolds of quantum channels and its application to quantum statistics
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DOI：
10.1088/1751-8113/41/25/255304
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发表时间：
2008-06-27
影响因子：
2.1
通讯作者：
Imai, Hiroshi
中科院分区：
文献类型：
--
作者：
Fujiwara, Akio;Imai, Hiroshi
在量子通道流形上引入光纤束结构。该结构与估计由参数theta指定的未知量子通道Gamma(theta)的问题密切相关。结果表明，在波浪号上的所有输入状态 (sigma) 上最大化的输出状态族 (id 圆乘以 Gamma(theta))((sigma) over tilde) 的量子 Fisher 信息，量化了参数 theta 的最终统计可区分性，并以纤维束上的几何量表示。利用该公式，导出了第n个扩展通道的最大量子Fisher信息(id圆乘以Gamma(theta))(圆乘以n)为O(n)的准则。该准则进一步证明，对于几乎所有量子通道，最大量子Fisher信息以O(n)量级增加。
A fibre bundle structure is introduced over manifolds of quantum channels. This structure has a close connection with the problem of estimating an unknown quantum channel Gamma(theta) specified by a parameter theta. It is shown that the quantum Fisher information of the family of output states (id circle times Gamma(theta))((sigma) over tilde) maximized over all input states (sigma) over tilde, which quantifies the ultimate statistical distinguishability of the parameter theta, is expressed in terms of a geometrical quantity on the fibre bundle. Using this formula, a criterion for the maximum quantum Fisher information of the nth extended channel (id circle times Gamma(theta))(circle times n) to be O(n) is derived. This criterion further proves that for almost all quantum channels, themaximum quantum Fisher information increases in the order of O(n).