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A fundamental tool to prove inner bounds in classical network information theory is the so-called conditional joint typicality lemma. In addition to the lemma, one often uses unions and intersections of typical sets in the inner bound…

Quantum Physics · Physics 2020-12-25 Pranab Sen

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

This paper presents a novel theoretical study of the general problem of multiple source adaptation using the notion of Renyi divergence. Our results build on our previous work [12], but significantly broaden the scope of that work in…

Machine Learning · Computer Science 2012-05-14 Yishay Mansour , Mehryar Mohri , Afshin Rostamizadeh

A set of classical or quantum states is equivalent to another one if there exists a pair of classical or quantum channels mapping either set to the other one. For dichotomies (pairs of states), this is closely connected to (classical or…

Quantum Physics · Physics 2024-07-09 Niklas Galke , Lauritz van Luijk , Henrik Wilming

This paper presents a one shot analysis of the lossy compression problem under average distortion constraints. We calculate the exact expected distortion of a random code. The result is given as an integral formula using a newly defined…

Information Theory · Computer Science 2020-05-18 Nir Elkayam , Meir Feder

Optimal rates for achieving an information processing task are often characterized in terms of regularized information measures. In many cases of quantum tasks, we do not know how to compute such quantities. Here, we exploit the symmetries…

Quantum Physics · Physics 2023-08-25 Omar Fawzi , Ala Shayeghi , Hoang Ta

The sandwiched R\'enyi divergences of two finite-dimensional density operators quantify their asymptotic distinguishability in the strong converse domain. This establishes the sandwiched R\'enyi divergences as the operationally relevant…

Quantum Physics · Physics 2025-08-12 Milán Mosonyi

R\'enyi divergence is related to R\'enyi entropy much like Kullback-Leibler divergence is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as a measure of information that satisfies almost the same…

Information Theory · Computer Science 2014-04-25 Tim van Erven , Peter Harremoës

We derive several efficiently computable converse bounds for quantum communication over quantum channels in both the one-shot and asymptotic regime. First, we derive one-shot semidefinite programming (SDP) converse bounds on the amount of…

Quantum Physics · Physics 2019-05-06 Xin Wang , Kun Fang , Runyao Duan

In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter…

Information Theory · Computer Science 2015-05-22 Si-Hyeon Lee , Sae-Young Chung

Lov\'asz's bound to the capacity of a graph and the the sphere-packing bound to the probability of error in channel coding are given a unified presentation as information radii of the Csisz\'ar type using the R{\'e}nyi divergence in the…

Information Theory · Computer Science 2013-05-21 Marco Dalai

A new proof of the direct part of the quantum channel coding theorem is shown based on a standpoint of quantum hypothesis testing. A packing procedure of mutually noncommutative operators is carried out to derive an upper bound on the error…

Quantum Physics · Physics 2007-05-23 Tomohiro Ogawa , Hiroshi Nagaoka

Given a general source with countably infinite source alphabet and a general channel with arbitrary abstract channel input/channel output alphabets, we study the joint source-channel coding problem from the information-spectrum point of…

Information Theory · Computer Science 2007-12-19 Te Sun Han

Given a general source $\sV=\{V^n\}\noi$ with {\em countably infinite} source alphabet and a general channel $\sW=\{W^n\}\noi$ with arbitrary {\em abstract} channel input and output alphabets, we study the joint source-channel coding…

Probability · Mathematics 2007-07-13 Te Sun Han

This paper introduces the induced divergence, a new quantum divergence measure that replaces the hypothesis testing divergence in position-based decoding, simplifying the analysis of quantum communication and state redistribution while…

Quantum Physics · Physics 2025-02-20 Gilad Gour

Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…

Quantum Physics · Physics 2021-08-11 Sisi Zhou , Zi-Wen Liu , Liang Jiang

The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during the last period, when a number of direct quantum coding theorems was discovered. To considerable extent…

Quantum Physics · Physics 2007-05-23 A. S. Holevo

Entanglement criteria for an $n$-partite quantum system with continuous variables are formulated in terms of R\'{e}nyi entropies. R\'{e}nyi entropies are widely used as a good information measure due to many nice properties. Derived…

Quantum Physics · Physics 2017-05-22 Alexey E. Rastegin

The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…

Information Theory · Computer Science 2015-03-17 C. M. F. Barros , Francisco Marcos de Assis , H. M. de Oliveira

Divergence chain rules for channels relate the divergence of a pair of channel inputs to the divergence of the corresponding channel outputs. An important special case of such a rule is the data-processing inequality, which tells us that if…

Quantum Physics · Physics 2024-05-21 Mario Berta , Marco Tomamichel