Upper continuity bounds on the relative -entropy for
arXiv:1010.1335 · doi:10.1063/1.3600535
Abstract
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative -entropy is generally unbounded for . Upper bounds on the quantum relative -entropy in terms of norm distances between its arguments are obtained in finite-dimensional context. These bounds characterize a continuity property in the sense of Fannes.
7 pages, no figures. The statements and the proofs from Section III are corrected. The results of Section IV are improved. Appendix A has been excluded
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- Continuity of quantum entropic quantities via almost convexity
- Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy
- Continuity of characteristics of composite quantum systems
- On unified-entropy characterization of quantum channels
- Upper continuity bound on the quantum quasi-relative entropy
- Continuity bounds for quantum entropies arising from a fundamental entropic inequality
- On directional derivatives of trace functionals of the form $A\mapsto\Tr(Pf(A))$