Sharp Continuity Bounds for Entropy and Conditional Entropy
Zhi-Hao Ma, Zhi-Hua Chen, Ismail Nikoufar,and Shao-Ming Fei
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Submission date: 15. Feb. 2017
published in: Science in China : physics, mechanics and astronomy, 60 (2017) 2, art-no. 020321
DOI number (of the published article): 10.1007/s11433-016-0367-x
PACS-Numbers: 03.65.Ud, 03.67.Mn
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We study the continuity estimation of the Tsallis entropy. An inequality relating the Tsallis entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed value of the trace norm distance. It includes the sharp Fannes inequality for von Neumann entropy as a special case.