相关论文: On maximization of measured $f$-divergence between…
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…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
The families of $f$-divergences (e.g. the Kullback-Leibler divergence) and Integral Probability Metrics (e.g. total variation distance or maximum mean discrepancies) are widely used to quantify the similarity between probability…
The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\'enyi divergences. Various quantum…
The problem of estimating the Kullback-Leibler divergence $D(P\|Q)$ between two unknown distributions $P$ and $Q$ is studied, under the assumption that the alphabet size $k$ of the distributions can scale to infinity. The estimation is…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…
We study the discrimination of N mixed quantum states in an optimal measurement that maximizes the probability of correct results while the probability of inconclusive results is fixed at a given value. After considering the discrimination…
A common way to discretize a probability measure is to use an empirical measure as a discrete approximation. But how far from being optimal is this approximation in the p-Wasserstein distance? In this paper, we study this question in two…
The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
Maximal quantum $f$-divergences, defined via the commutant Radon--Nikodym derivative, form a fundamental class of distinguishability measures for quantum states associated with operator convex functions. In this paper, we study the…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…
Explicit classical states achieving maximal $f$-divergence are given, allowing for a simple proof of Matsumoto's Theorem, and the systematic extension of any inequality between classical $f$-divergences to quantum $f$-divergences. Our…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
We present the first experimental demonstration of the maximum confidence measurement strategy for quantum state discrimination. Applying this strategy to an arbitrary set of states assigns to each input state a measurement outcome which,…
Empirical divergence maximization (EDM) refers to a recently proposed strategy for estimating f-divergences and likelihood ratio functions. This paper extends the idea to empirical vector quantization where one seeks to empirically derive…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…