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Related papers: Smooth Renyi Entropies and the Quantum Information…

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The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is…

Quantum Physics · Physics 2017-01-11 Zhihua Chen , Zhihao Ma , Ismail Nikoufar , Shaoming Fei

A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each…

Quantum Physics · Physics 2007-07-13 Nilanjana Datta , Yuri Suhov

In this paper, we show an interesting connection between a quantum sampling technique and quantum uncertainty. Namely, we use the quantum sampling technique, introduced by Bouman and Fehr, to derive a novel entropic uncertainty relation…

Quantum Physics · Physics 2021-02-05 Walter O. Krawec

We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…

Differential Geometry · Mathematics 2026-01-21 Amandip Sangha

We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…

Quantum Physics · Physics 2024-11-20 Simon Becker , Nilanjana Datta , Michael G. Jabbour

Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…

Quantum Physics · Physics 2020-01-03 R. V. Ramos

We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical…

Quantum Physics · Physics 2009-10-28 Christopher King , Andrzej Lesniewski

Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…

Quantum Physics · Physics 2023-07-19 Tongyang Li , Xiaodi Wu

We study how the Shannon entropy of sequences produced by an information source converges to the source's entropy rate. We synthesize several phenomenological approaches to applying information theoretic measures of randomness and memory to…

Statistical Mechanics · Physics 2007-05-23 James P. Crutchfield , David P. Feldman

For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for…

Quantum Physics · Physics 2015-06-19 Margarita A Man'ko , Vladimir I Man'ko

Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…

Quantum Physics · Physics 2021-11-23 Tom Gur , Min-Hsiu Hsieh , Sathyawageeswar Subramanian

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

Quantum Physics · Physics 2019-08-27 Christoph Hirche , David Reeb

Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…

Quantum Physics · Physics 2009-11-07 V. Vedral

Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we…

Physics and Society · Physics 2016-12-23 Manlio De Domenico , Jacob Biamonte

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…

Quantum Physics · Physics 2026-04-29 Bartosz Regula , Ludovico Lami , Nilanjana Datta

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

Information Theory · Computer Science 2024-05-07 Mokshay Madiman , Prasad Tetali

We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…

Information Theory · Computer Science 2019-11-25 David J. Galas

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

It is well-known that von Neumann entropy is nonmonotonic unlike Shannon entropy (which is monotonically nondecreasing). Consequently, it is difficult to relate the entropies of the subsystems of a given quantum state. In this paper, we…

Quantum Physics · Physics 2011-04-07 Pradeep Sarvepalli

The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…

Quantum Physics · Physics 2013-05-24 Pablo Sánchez-Moreno , Steeve Zozor , Jesus S. Dehesa