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Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact…

Quantum Physics · Physics 2010-07-08 Fernando G. S. L. Brandao , Michal Horodecki

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

Quantum Physics · Physics 2025-01-09 Michael G. Jabbour , Nilanjana Datta

We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…

Quantum Physics · Physics 2016-09-08 Andreas Winter

We reply to the Comment by Jizba and Korbel [arXiv:1905.00729v1] by first pointing out that the Schur-concavity proposed by them falls short of identifying the correct intervals of normalization for the optimum probability distribution even…

Statistical Mechanics · Physics 2019-08-28 Thomas Oikonomou , G. Baris Bagci

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…

Quantum Physics · Physics 2016-09-06 Andreas Winter

This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and…

Information Theory · Computer Science 2024-08-20 Huiyuan Yang , Yuxuan Shi , Shuo Shao , Xiaojun Yuan

B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…

Quantum Physics · Physics 2008-08-08 Alexei Kaltchenko

We show how the renormalization group approach can be used to prove quantitative central limit theorems (CLTs) in the setting of free, Boolean, bi-free and bi-Boolean independence under finite third moment assumptions. The proofs rely on…

Probability · Mathematics 2026-03-30 Jad Hamdan

A natural measure for the amount of quantum information that a physical system E holds about another system A = A_1,...,A_n is given by the min-entropy Hmin(A|E). Specifically, the min-entropy measures the amount of entanglement between E…

Quantum Physics · Physics 2015-06-16 Frédéric Dupuis , Omar Fawzi , Stephanie Wehner

Recently, Anshu et al. introduced "partially" smoothed information measures and used them to derive tighter bounds for several information-processing tasks, including quantum state merging and privacy amplification against quantum…

Quantum Physics · Physics 2021-06-29 Dina Abdelhadi , Joseph M. Renes

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…

Machine Learning · Statistics 2022-03-29 Borja Rodríguez-Gálvez , Germán Bassi , Ragnar Thobaben , Mikael Skoglund

The aim of the paper is to study the link between non additivity of some entropies and their boundedness. We propose an axiomatic construction of the entropy relying on the fact that entropy belongs to a group isomorphic to the usual…

Statistical Mechanics · Physics 2009-11-11 Pierre-Olivier Amblard , Christophe Vignat

The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…

Quantum Physics · Physics 2025-06-05 Kun Fang , Hamza Fawzi , Omar Fawzi

The entropy accumulation theorem states that the smooth min-entropy of an $n$-partite system $A = (A_1, \ldots, A_n)$ is lower-bounded by the sum of the von Neumann entropies of suitably chosen conditional states up to corrections that are…

Quantum Physics · Physics 2019-07-23 Frédéric Dupuis , Omar Fawzi

From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…

Information Theory · Computer Science 2018-08-01 Arash Atashpendar , David Mestel , A. W. Roscoe , Peter Y. A. Ryan

Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently…

Quantum Physics · Physics 2026-05-27 Sreejith Sreekumar , Ziv Goldfeld , Mark M. Wilde

We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…

Systems and Control · Electrical Eng. & Systems 2023-11-14 Hussein Sibai , Sayan Mitra

Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…

Information Theory · Computer Science 2017-01-04 Günther Koliander , Georg Pichler , Erwin Riegler , Franz Hlawatsch

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

Mathematical Physics · Physics 2018-03-02 Alberto Barchielli , Matteo Gregoratti , Alessandro Toigo

We consider an extension of $\epsilon$-entropy to a KL-divergence based complexity measure for randomized density estimation methods. Based on this extension, we develop a general information-theoretical inequality that measures the…

Statistics Theory · Mathematics 2007-06-13 Tong Zhang