Some general properties of unified entropies

Details Some general properties of unified entropies Some general properties of unified entropies

2010-12-24

arxiv.org/abs/1012.5356v3

J. Stat. Phys. 143, 1120-1135 (2011)

Physics

Quantum Physics

11 pages, no figures. Minor grammatical changes are made. To appear in J. Stat. Phys

Scientific paper

10.1007/s10955-011-0231-x

Basic properties of the unified entropies are examined. The consideration is mainly restricted to the finite-dimensional quantum case. Bounds in terms of ensembles of quantum states are given. Both the continuity in Fannes' sense and stability in Lesche's sense are shown for wide ranges of parameters. In particular, uniform estimates are obtained for the quantum R\'{e}nyi entropies. Stability properties in the thermodynamic limit are discussed as well. It is shown that the unified entropies enjoy both the subadditivity and triangle inequality for a certain range of parameters. Non-decreasing of all the unified entropies under projective measurement is proved.

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