## 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)].

### MSC:

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

quantum entropy

Zbl 0178.22401
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### 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
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