Raggio, G. A. Properties of \(q\)-entropies. (English) Zbl 0853.94013 J. Math. Phys. 36, No. 9, 4785-4791 (1995). Basic properties are proven for the quantum entropy of order \(q\) \((q\)-entropy) \(S_q (\rho) = (\rho - 1)^{-1} (1 - \text{tr} (\rho^q))\), \(0 < q \neq 1\). Concavity, quasi-concavity, and continuity hold, but additivity and subadditivity do not apply. This quantum entropy is the parallel to the entropy of order \(\alpha\) first introduced in the literature by J. Havrada and F. Charvat [in “Quantification method of classification processes. Concept of structural \(\alpha\)-entropy”, Kybernetica (Prague), 3, 30-35 (1967; Zbl 0178.22401)]. Reviewer: G.Jumarie (Montreal) Cited in 2 ReviewsCited in 17 Documents MSC: 94A17 Measures of information, entropy 81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy Keywords:quantum entropy Citations:Zbl 0178.22401 PDF BibTeX XML Cite \textit{G. A. Raggio}, J. Math. Phys. 36, No. 9, 4785--4791 (1995; Zbl 0853.94013) Full Text: DOI OpenURL References: [1] DOI: 10.1016/S0019-9958(70)80040-7 · Zbl 0205.46901 [2] DOI: 10.1103/RevModPhys.50.221 [3] DOI: 10.1007/BF01016429 · Zbl 1082.82501 [4] DOI: 10.1088/0305-4470/24/2/004 [5] DOI: 10.1007/BF02771613 · Zbl 0156.37902 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.