Some General Properties of Unified Entropies |
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Authors: | Alexey E Rastegin |
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Institution: | (1) School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada |
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Abstract: | 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 Rényi 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 measurements is proved. |
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Keywords: | |
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