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 ? 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 ? q ? 2, Fano type quantum inequalities with freely variable parameters are obtained.
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