Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification

Details Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification

2003-01-24

arxiv.org/abs/quant-ph/0301136v1

Physics

Quantum Physics

11 pages, no figures

Scientific paper

10.1103/PhysRevA.68.032302

The Kullback-Leibler divergence offers an information-theoretic basis for measuring the difference between two given distributions. Its quantum analog, however, fails to play a corresponding role for comparing two density matrices, if the reference states are pure states. Here, it is shown that nonadditive (nonextensive) generalization of quantum information theory is free from such a difficulty and the associated quantity, termed the quantum q-divergence, can in fact be a good information-theoretic measure of the degree of purification. The correspondence relation between the ordinary divergence and the q-divergence is violated for the pure reference states, in general.

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