From f-divergence to quantum quasi-entropies and their use

Details From f-divergence to quantum quasi-entropies and their use From f-divergence to quantum quasi-entropies and their use

2009-09-20

arxiv.org/abs/0909.3647v1

Computer Science

Information Theory

Written version of the lecture in the conference "Information and Communication" held in Budapest

Scientific paper

Csiszar's f-divergence of two probability distributions was extended to the quantum case by the author in 1985. In the quantum setting positive semidefinite matrices are in the place of probability distributions and the quantum generalization is called quasi-entropy which is related to some other important concepts as covariance, quadratic costs, Fisher information, Cramer-Rao inequality and uncertainty relation. A conjecture about the scalar curvature of a Fisher information geometry is explained. The described subjects are overviewed in details in the matrix setting, but at the very end the von Neumann algebra approach is sketched shortly.

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