Direct approach to quantum extensions of Fisher information
Direct approach to quantum extensions of Fisher information
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DOI：
10.1007/s11464-007-0023-4
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发表时间：
2007-09
影响因子：
--
通讯作者：
Chen Ping;Shun-Long Luo
中科院分区：
文献类型：
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作者：
Chen Ping;Shun-Long Luo
通过操纵经典的Fisher信息和采用各种导数的密度算子，并使用完全直观和直接的方法，我们介绍了两个家庭的量子扩展的Fisher信息，包括那些定义通过对称对数导数，通过右对数导数，通过Bogoliubov-Kubo-Mori的衍生物，以及通过衍生商的条件下，作为特殊情况。研究了Fisher信息的量子扩展的一些基本性质，建立了一个多参数量子Cramér-Rao不等式，并举例说明了其在量子测不准中的应用.
By manipulating classical Fisher information and employing various derivatives of density operators, and using entirely intuitive and direct methods, we introduce two families of quantum extensions of Fisher information that include those defined via the symmetric logarithmic derivative, via the right logarithmic derivative, via the Bogoliubov-Kubo-Mori derivative, as well as via the derivative in terms of commutators, as special cases. Some fundamental properties of these quantum extensions of Fisher information are investigated, a multi-parameter quantum Cramér-Rao inequality is established, and applications to characterizing quantum uncertainty are illustrated.