A generalized quantum relative entropy

Luiza H. F. Andrade; Rui F. Vigelis; Charles C. Cavalcante

doi:10.3934/amc.2020063

Article Contents

2020, Volume 14, Issue 3: 413-422. Doi: 10.3934/amc.2020063

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A generalized quantum relative entropy

1.
Department of Natural Sciences, Mathematics and Statistics, Federal Rural University of the Semi-arid Region, Mossoró-RN, Brazil
2.
Computer Engineering, Campus Sobral, Federal University of Ceará, Sobral-CE, Brazil
3.
Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza-CE, Brazil

^* Corresponding author: Luiza H. F. Andrade
^* Corresponding author: Luiza H. F. Andrade

Received: December 2018

Revised: September 2019

Early access: January 2020

Published: August 2020

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Abstract

We propose a generalization of the quantum relative entropy by considering the geodesic on a manifold formed by all the invertible density matrices $ \mathcal{P} $. This geodesic is defined from a deformed exponential function $ \varphi $ which allows to work with a wider class of families of probability distributions. Such choice allows important flexibility in the statistical model. We show and discuss some properties of this proposed generalized quantum relative entropy.

Keywords:

Quantum relative entropy,
quantum information theory,
deformed exponential function,
$ \varphi $-families of probablity distributions.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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