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Related papers: Test-measured R\'enyi divergences

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R\'enyi entropy of order \alpha is a general measure of entropy. In this paper we derive estimations for the R\'enyi entropy of the mixture of sources in terms of the entropy of the single sources. These relations allow to compute the…

Information Theory · Computer Science 2012-04-13 Marek Śmieja , Jacek Tabor

The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity property for the coherence measures…

Quantum Physics · Physics 2017-08-02 Lian-He Shao , Yongming Li , Yu Luo , Zhengjun Xi

The R\'enyi information measures are characterized in terms of their Shannon counterparts, and properties of the former are recovered from first principle via the associated properties of the latter. Motivated by this characterization, a…

Information Theory · Computer Science 2016-03-14 Ofer Shayevitz

For $\alpha,z>0$ with $\alpha\ne1$, motivated by comparison between different kinds of R\'enyi divergences in quantum information, we consider log-majorization between the matrix functions \begin{align*}…

Functional Analysis · Mathematics 2018-08-14 Fumio Hiai

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare…

Statistics Theory · Mathematics 2020-09-08 Xiaosheng Mu , Luciano Pomatto , Philipp Strack , Omer Tamuz

Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…

Quantum Physics · Physics 2025-12-23 Adam Brandenburger , Pierfrancesco La Mura

Disagreement is an essential element of science and life in general. The language of probabilities and statistics is often used to describe disagreements quantitatively. In practice, however, we want much more than that. We want…

General Finance · Quantitative Finance 2020-09-01 Andrei N. Soklakov

We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a…

Quantum Physics · Physics 2026-03-31 Satvik Singh , Bjarne Bergh

R\'enyi and Augustin information are generalizations of mutual information defined via the R\'enyi divergence, playing a significant role in evaluating the performance of information processing tasks by virtue of its connection to the error…

Quantum Physics · Physics 2022-05-31 Hao-Chung Cheng , Li Gao , Min-Hsiu Hsieh

In this paper, we examine the existence of the R\'enyi divergence between two time invariant general hidden Markov models with arbitrary positive initial distributions. By making use of a Markov chain representation of the probability…

Information Theory · Computer Science 2021-06-04 Cheng-Der Fuh , Su-Chi Fuh , Yuan-Chen Liu , Chuan-Ju Wang

We show that for any $\alpha>0$ the R\'enyi entropy of order $\alpha$ is minimized, among all symmetric log-concave random variables with fixed variance, either for a uniform distribution or for a two sided exponential distribution. The…

Information Theory · Computer Science 2021-10-05 Maciej Białobrzeski , Piotr Nayar

Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the R\'enyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation…

Populations and Evolution · Quantitative Biology 2016-12-26 Thierry Mora , Aleksandra M. Walczak

This paper studies forward and reverse projections for the R\'{e}nyi divergence of order $\alpha \in (0, \infty)$ on $\alpha$-convex sets. The forward projection on such a set is motivated by some works of Tsallis {\em et al.} in…

Information Theory · Computer Science 2016-07-27 M. Ashok Kumar , Igal Sason

The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a…

Quantum Physics · Physics 2009-10-31 Anthony Chefles

The discrimination of two nonorthogonal states is a fundamental element for secure and efficient communication. Quantum measurements of nonorthogonal coherent states can enhance information transfer beyond the limits of conventional…

Quantum Physics · Physics 2018-07-16 M. T. DiMario , F. E. Becerra

This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…

Information Theory · Computer Science 2017-02-09 Maciej Skorski

Uhlmann's theorem is a cornerstone of quantum information theory, stating that for any quantum state $\rho_{AB}$ and any state $\sigma_A$, there exists an extension $\sigma_{AB}$ of $\sigma_A$ such that the fidelity between $\rho_{AB}$ and…

Quantum Physics · Physics 2026-03-03 Kun Fang , Hamza Fawzi , Omar Fawzi

We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…

Quantum Physics · Physics 2021-10-04 Alexander McKinlay

Quantum state discrimination depicts the general progress of extracting classical information from quantum systems. We show that quantum state discrimination can be realized in a device-independent scenario using tools of self-testing…

Quantum Physics · Physics 2024-01-25 Xinyu Qiu , Lin Chen

The conditional quantum mutual information $I(A;B|C)$ of a tripartite state $\rho_{ABC}$ is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is…

Quantum Physics · Physics 2015-03-17 Mario Berta , Kaushik P. Seshadreesan , Mark M. Wilde