Continuity and Stability of Partial Entropic Sums

Abstract

Extensions of Fannes' inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced entropic measures and some applications are discussed. The derived estimates provide a complete characterization of the continuity and stability properties in the refined scale. The results are also reformulated in terms of Uhlmann's partial fidelities.

9 pages, no figures. Some explanatory and technical improvements are made. The bibliography is extended. Detected errors and typos are corrected

References in corpus (4)

• Subadditivity of q-entropies for q>1
• A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
• A generalized Fannes inequality
• Bounds on Shannon distinguishability in terms of partitioned measures

Cited by in corpus (8)

• Some general properties of unified entropies
• Relations for certain symmetric norms and anti-norms before and after partial trace
• Entropic uncertainty relations for extremal unravelings of super-operators
• Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy
• Sharp Continuity Bounds for Entropy and Conditional Entropy
• Upper continuity bounds on the relative $q$-entropy for $q>1$
• On unified-entropy characterization of quantum channels
• Fano type quantum inequalities in terms of $q$-entropies