关于Tsallis相对熵的界和广义斜信息的一个不等式
On bounds of Tsallis relative entropy and an inequality for generalized skew information
摘要：
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定义的，因此迹不等式在量子信息科学中的数学理论发展中往往起着重要的作用。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相对熵的单参数推广Tsallis相对熵的上界和下界.此外，我们比较了已知的界限和新的界限，分别为上限和下界。通过引入广义相关测度，给出了广义斜信息的一个不等式。
英文摘要：
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this paper, we study some properties for information quantities in quantum system through trace inequalities. Especially, we give upper bounds and lower bounds of Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum system. 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.
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