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Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…

Information Theory · Computer Science 2026-02-02 Roberto Rubboli , Erkka Haapasalo , Marco Tomamichel

Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in…

Information Theory · Computer Science 2020-11-10 Christoph Hirche

The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…

Information Theory · Computer Science 2020-07-15 Lampros Gavalakis , Ioannis Kontoyiannis

There are no universally accepted definitions of R\'enyi conditional entropy and R\'enyi mutual information, although motivated by different applications, several definitions have been proposed in the literature. In this paper, we consider…

Information Theory · Computer Science 2025-11-05 Shi-Bing Li , Ke Li , Lei Yu

This paper considers the problem of soft guessing under a logarithmic loss distortion measure while allowing errors. We find an optimal guessing strategy, and derive single-shot upper and lower bounds for the minimal guessing moments as…

Information Theory · Computer Science 2025-10-13 Shota Saito , Hamdi Joudeh

We evaluate the asymptotics of equivocations, their exponents as well as their second-order coding rates under various R\'{e}nyi information measures. Specifically, we consider the effect of applying a hash function on a source and we…

Information Theory · Computer Science 2016-07-06 Masahito Hayashi , Vincent Y. F. Tan

The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. In this paper, we derive the exact exponent for the asymptotic decay of the small modification of the quantum state in smoothing the…

Quantum Physics · Physics 2023-06-02 Ke Li , Yongsheng Yao , Masahito Hayashi

Based on the problem of quantum data compression in a lossless way, we present here an operational interpretation for the family of quantum R\'enyi entropies. In order to do this, we appeal to a very general quantum encoding scheme that…

Quantum Physics · Physics 2017-10-05 G. Bellomo , G. M. Bosyk , F. Holik , S. Zozor

This work gives the asymptotic error distribution of the stochastic Runge--Kutta (SRK) method of strong order $1$ applied to Stratonovich-type stochastic differential equations. For dealing with the implicitness introduced in the diffusion…

Numerical Analysis · Mathematics 2025-08-05 Diancong Jin

A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…

Information Theory · Computer Science 2026-04-16 Terence Viaud , Ioannis Kontoyiannis

In the last few years, there has been a great interest in extending the information-theoretic scenario for the non-asymptotic or one-shot case, i.e., where the channel is used only once. We provide the one-shot rate region for the…

Information Theory · Computer Science 2013-02-26 Naresh Sharma , Naqueeb Ahmad Warsi

We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum…

Quantum Physics · Physics 2013-12-11 Nilanjana Datta , Milan Mosonyi , Min-Hsiu Hsieh , Fernando G. S. L. Brandao

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…

Statistics Theory · Mathematics 2021-06-18 Abhik Ghosh , Ayanendranath Basu

In this work, we prove uniform continuity bounds for entropic quantities related to the sandwiched R\'enyi divergences such as the sandwiched R\'enyi conditional entropy. We follow three different approaches: The first one is the "almost…

Quantum Physics · Physics 2025-05-08 Andreas Bluhm , Ángela Capel , Paul Gondolf , Tim Möbus

Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…

Statistics Theory · Mathematics 2011-03-28 David Källberg , Nikolaj Leonenko , Oleg Seleznjev

Traditional asymptotic information-theoretic studies of the fundamental limits of wireless communication systems primarily rely on some ideal assumptions, such as infinite blocklength and vanishing error probability. While these assumptions…

Information Theory · Computer Science 2025-12-29 Junyuan Gao , Shuao Chen , Yongpeng Wu , Liang Liu , Giuseppe Caire , H. Vincent Poor , Wenjun Zhang

Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…

Quantum Physics · Physics 2023-05-31 G. W. Forbes , Miguel A. Alonso

This paper establishes the exact strong converse exponent of the soft covering problem in the classical setting. This exponent characterizes the slowest achievable convergence speed of the total variation to one when a code of rate below…

Information Theory · Computer Science 2026-04-01 Xingyi He , S. Sandeep Pradhan , Andreas Winter

Consider a sequential process in which each step outputs a system $A_i$ and updates a side information register $E$. We prove that if this process satisfies a natural "non-signalling" condition between past outputs and future side…

Quantum Physics · Physics 2023-01-18 Tony Metger , Omar Fawzi , David Sutter , Renato Renner

Two typical fixed-length random number generation problems in information theory are considered for general sources. One is the source resolvability problem and the other is the intrinsic randomness problem. In each of these problems, the…

Information Theory · Computer Science 2024-05-14 Ryo Nomura , Hideki Yagi