# A new quantum version of f-divergence

@article{Matsumoto2013ANQ, title={A new quantum version of f-divergence}, author={Keiji Matsumoto}, journal={arXiv: Quantum Physics}, year={2013} }

This paper proposes and studies new quantum version of $f$-divergences, a class of convex functionals of a pair of probability distributions including Kullback-Leibler divergence, Rnyi-type relative entropy and so on. There are several quantum versions so far, including the one by Petz. We introduce another quantum version ($\mathrm{D}_{f}^{\max}$, below), defined as the solution to an optimization problem, or the minimum classical $f$- divergence necessary to generate a given pair of quantum… Expand

#### 39 Citations

Different quantum f-divergences and the reversibility of quantum operations

- Mathematics, Physics
- 2016

This paper compares the standard and the maximal $f-divergences regarding their ability to detect the reversibility of quantum operations, and studies the monotonicity of the Renyi divergences under the special class of bistochastic maps that leave one of the arguments of theRenyi divergence invariant. Expand

On variational expressions for quantum relative entropies

- Mathematics, Physics
- ArXiv
- 2015

A new variational expression is created for the measured Rényi relative entropy, which is exploited to show that certain lower bounds on quantum conditional mutual information are superadditive. Expand

Reversibility of distance mesures of states with some focus on total variation distance.

- Physics, Mathematics
- 2019

Consider a classical system, which is in the state described by probability distribution $p$ or $q$, and embed these classical informations into quantum system by a physical map $\Gamma$,… Expand

Relations between different quantum R\'enyi divergences.

- Physics
- 2020

Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in quantum information processing. Two families of such generalizations turn out to be… Expand

Optimized Quantum F-Divergences

- Computer Science, Physics
- 2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

The optimized quantum $f-divergence is introduced as a related generalization of quantum relative entropy and it is proved that it satisfies the data processing inequality, and the method of proof relies upon the operator Jensen inequality, similar to Petz's original approach. Expand

Quantum Hellinger distances revisited

- Mathematics, Physics
- 2019

This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the… Expand

Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

- Computer Science, Mathematics
- ArXiv
- 2019

A chain rule inequality that immediately implies the "amortization collapse" for the geometric R\'enyi divergence is proved, addressing an open question by Berta et al. in the area of quantum channel discrimination. Expand

Optimized quantum f-divergences and data processing

- Mathematics, Physics
- ArXiv
- 2017

The optimized quantum f-divergence is introduced as a related generalization of quantum relative entropy and it is proved that it satisfies the data processing inequality, and the method of proof relies upon the operator Jensen inequality, similar to Petz's original approach. Expand

Concentration of quantum states from quantum functional and Talagrand inequalities

- Mathematics
- 2017

Quantum functional inequalities (e.g. the logarithmic Sobolev- and Poincar\'{e} inequalities) have found widespread application in the study of the behavior of ergodic quantum Markov semigroups. The… Expand

The α → 1 limit of the Sharp Quantum Rényi Divergence

- 2021

Fawzi and Fawzi [1] recently defined the sharp Rényi divergence, D α , for α ∈ (1,∞), as an additional quantum Rényi divergence with nice mathematical properties and applications in quantum channel… Expand

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