Properties of \(q\)-entropies. (English) Zbl 0853.94013

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)].


94A17 Measures of information, entropy
81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy


quantum entropy


Zbl 0178.22401
Full Text: DOI


[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
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