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

Abstract

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.

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

References in corpus (3)

• Metric adjusted skew information
• Uncertainty Principle and Quantum Fisher Information - II
• Uncertainty principle with quantum Fisher information

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• Quantum f-divergences and error correction
• Entropy: The Markov Ordering Approach
• Optimized quantum f-divergences and data processing
• Partial separability revisited: Necessary and sufficient criteria
• On convex optimization problems in quantum information theory
• A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the $q$-$z$ Family
• Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy
• Recoverability for Holevo's just-as-good fidelity