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• W3104337654 abstract "Pinsker’s and Fannes’ type bounds on the Tsallis relative entropy are derived. The monotonicity property of the quantum f -divergence is used fot its estimation from below. For order (alpha in (0,1)), a family of lower bounds of Pinsker type is obtained. For (alpha >1) and the commutative case, upper continuity bounds on the relative entropy in terms of the minimal probability in its second argument are derived. Both the lower and upper bounds presented are reformulated for the case of Rényi’s entropies. The Fano inequality is extended to Tsallis’ entropies for all (alpha >0). The deduced bounds on the Tsallis conditional entropy are used to obtain inequalities of Fannes’ type." @default.
• W3104337654 created "2020-11-23" @default.
• W3104337654 creator A5004803532 @default.
• W3104337654 date "2013-05-10" @default.
• W3104337654 modified "2023-10-17" @default.
• W3104337654 title "Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy" @default.
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• W3104337654 doi "https://doi.org/10.1007/s11040-013-9128-z" @default.
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