Inequalities for Tsallis relative entropy and generalized skew information
Inequalities for Tsallis relative entropy and generalized skew information
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DOI：
10.1080/03081087.2011.574624
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发表时间：
2011-09
影响因子：
1.1
通讯作者：
S. Furuichi
中科院分区：
文献类型：
--
作者：
S. Furuichi
量子熵和斜信息在量子信息科学中起着重要的作用。它们是由正算子的迹所定义的，因此迹不等式在量子信息科学的数学理论发展中具有重要的作用。本文利用迹不等式研究了量子系统中信息量的一些性质。特别地，我们给出了量子系统中Tsallis相对熵的上界和下界，Tsallis相对熵是量子系统中相对熵的单参数推广。此外，我们比较了已知的界限和新的界限，分别为上限和下限。通过引入广义相关测度，给出了广义斜信息的一个不等式。
Quantum entropy and skew information play important roles in quantum information science. They are defined by traces of positive operators, hence trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this article, we study some properties for information quantities in quantum systems through trace inequalities. Especially, we give upper bounds and lower bounds on the Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum systems. In addition, we compare the known bounds and the new bounds, for both upper and lower bounds, respectively. We also give an inequality for generalized skew information by introducing a generalized correlation measure.