Fano type quantum inequalities in terms of $q$-entropies

Abstract

Generalizations of the quantum Fano inequality are considered. The notion of $q$-entropy exchange is introduced. This quantity is concave in each of its two arguments. For $q\ge 0$, the inequality of Fano type with $q$-entropic functionals is established. The notion of coherent information and the perfect reversibility of a quantum operation are discussed in the context of $q$-entropies. By the monotonicity property, the lower bound of Pinsker type in terms of the trace norm distance is obtained for the Tsallis relative $q$-entropy of order $q=1/2$. For $0\le q\le 2$, Fano type quantum inequalities with freely variable parameters are obtained.

10 pages, no figures. A partly incorrect statement of Section III is replaced with the valid one. Detected typos are corrected. The bibliography is extended and updated

References in corpus (4)

• Some extensions of the uncertainty principle
• Some general properties of unified entropies
• Continuity bounds on the quantum relative entropy - II
• Continuity and Stability of Partial Entropic Sums