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Related papers: Strong converse theorems using R\'enyi entropies

200 papers

Concepts of information theory are increasingly used to characterize collective phenomena in condensed matter systems, such as the use of entanglement entropies to identify emergent topological order in interacting quantum many-body…

Strongly Correlated Electrons · Physics 2015-09-28 Johannes Helmes , Jean-Marie Stéphan , Simon Trebst

A variety of new measures of quantum Renyi mutual information and quantum Renyi conditional entropy have recently been proposed, and some of their mathematical properties explored. Here, we show that the Renyi mutual information attains…

Quantum Physics · Physics 2016-10-20 Masahito Hayashi , Marco Tomamichel

The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…

Machine Learning · Computer Science 2022-12-01 Yuxin Dong , Tieliang Gong , Shujian Yu , Hong Chen , Chen Li

We explore a large class of correlation measures called the $\alpha-z$ R\'enyi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of R\'enyi entropies, the $\alpha-z$ RMIs are positive…

High Energy Physics - Theory · Physics 2024-08-27 Jonah Kudler-Flam , Laimei Nie , Akash Vijay

The Polyanskiy-Verd\'{u} paradigm provides an elegant way of using generalized-divergences to obtain strong converses and thus far has remained confined to protocols involving channels (classical or quantum). In this paper, drawing…

Quantum Physics · Physics 2014-04-24 Naresh Sharma

We determine the exact strong converse exponent of classical-quantum channel coding, for every rate above the Holevo capacity. Our form of the exponent is an exact analogue of Arimoto's, given as a transform of the Renyi capacities with…

Quantum Physics · Physics 2018-07-10 Milan Mosonyi , Tomohiro Ogawa

We present a new scheme for the compression of one-way quantum messages, in the setting of coherent entanglement assisted quantum communication. For this, we present a new technical tool that we call the convex split lemma, which is…

Quantum Physics · Physics 2017-09-27 Anurag Anshu , Vamsi Krishna Devabathini , Rahul Jain

It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…

Quantum Physics · Physics 2023-07-07 Michael J. W. Hall

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the R\'enyi entropy is presented that uses transport arguments from normal densities and a change of variable by…

Information Theory · Computer Science 2018-10-17 Olivier Rioul

We prove that several known upper bounds on the classical capacity of thermal and additive noise bosonic channels are actually strong converse rates. Our results strengthen the interpretation of these upper bounds, in the sense that we now…

Quantum Physics · Physics 2014-07-29 Bhaskar Roy Bardhan , Mark M. Wilde

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

We introduce a variant of the R\'enyi entropy definition that aligns it with the well-known H\"older mean: in the new formulation, the r-th order R\'enyi Entropy is the logarithm of the inverse of the r-th order H\"older mean. This brings…

Information Theory · Computer Science 2018-11-16 Francisco José Valverde-Albacete , Carmen Peláez-Moreno

Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to…

Quantum Physics · Physics 2013-03-20 Sebastian Meznaric

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

The mutual information is a measure of classical and quantum correlations of great interest in quantum information. It is also relevant in quantum many-body physics, by virtue of satisfying an area law for thermal states and bounding all…

Quantum Physics · Physics 2021-09-15 Samuel O. Scalet , Álvaro M. Alhambra , Georgios Styliaris , J. Ignacio Cirac

We prove a tight uniform continuity bound for Arimoto's version of the conditional $\alpha$-R\'enyi entropy, for the range $\alpha \in [0, 1)$. This definition of the conditional R\'enyi entropy is the most natural one among the multiple…

Information Theory · Computer Science 2022-03-29 Michael G. Jabbour , Nilanjana Datta

Quantum privacy amplification is a central task in quantum cryptography. Given shared randomness, which is initially correlated with a quantum system held by an eavesdropper, the goal is to extract uniform randomness which is decoupled from…

Quantum Physics · Physics 2022-02-23 Robert Salzmann , Nilanjana Datta

Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in…

Quantum Physics · Physics 2015-04-10 Mario Berta , Kaushik P. Seshadreesan , Mark M. Wilde

This work explores properties of Strong Data-Processing constants for R\'enyi Divergences. Parallels are made with the well-studied $\varphi$-Divergences, and it is shown that the order $\alpha$ of R\'enyi Divergences dictates whether…

Information Theory · Computer Science 2026-01-15 Adrien Vandenbroucque , Amedeo Roberto Esposito , Michael Gastpar

The paper presents exponentially-strong converses for source-coding, channel coding, and hypothesis testing problems. More specifically, it presents alternative proofs for the well-known exponentially-strong converse bounds for almost…

Information Theory · Computer Science 2023-01-18 Mustapha Hamad , Michele Wigger , Mireille Sarkiss