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

Alexey E. Rastegin

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

Quantum Physics 2011-09-27 v3

Authors: Alexey E. Rastegin

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 $q\geq0$ , 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 $0\leq{q}\leq2$ , Fano type quantum inequalities with freely variable parameters are obtained.

Keywords

quantum Fano inequality q-entropy q-entropy exchange coherent information quantum operation Tsallis relative q-entropy Pinsker inequality

Cite

@article{arxiv.1010.1811,
  title  = {Fano type quantum inequalities in terms of $q$-entropies},
  author = {Alexey E. Rastegin},
  journal= {arXiv preprint arXiv:1010.1811},
  year   = {2011}
}

Comments

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

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

Abstract

Keywords

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