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Fano type quantum inequalities in terms of \(q\)-entropies. (English) Zbl 1263.81093
Summary: 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 \(q \geq 0\), 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 \(0 \leq q \leq 2\), Fano type quantum inequalities with freely variable parameters are obtained.

MSC:
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
94A17 Measures of information, entropy
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