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We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…

Metric Geometry · Mathematics 2020-12-17 Tom Leinster , Emily Roff

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Information Theory · Computer Science 2021-09-22 Gilad Gour , Marco Tomamichel

The field of information science has greatly developed, and applications in various fields have emerged. In this paper, we evaluated the coding system in the theory of Tsallis entropy for transmission of messages and aimed to formulate the…

Molecular Networks · Quantitative Biology 2017-12-13 Tatsuaki Tsuruyama

Traditional thermodynamic trade-off relations usually apply to quantities that depend linearly on probability distributions. In contrast, many important information-theoretic measures, such as entropies, are nonlinear and therefore…

Statistical Mechanics · Physics 2026-02-17 Yoshihiko Hasegawa

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

This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…

Information Theory · Computer Science 2016-11-17 Igal Sason

We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…

Quantum Physics · Physics 2019-12-10 Wallas S. Nascimento , Marcos M. de Almeida , Frederico V. Prudente

Shannon entropy, a cornerstone of information theory, statistical physics and inference methods, is uniquely identified by the Shannon-Khinchin or Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the study of…

Data Analysis, Statistics and Probability · Physics 2026-04-20 Andrea Somazzi , Diego Garlaschelli

We propose entropic measures for the strength of single-particle and two-particle interference in interferometric experiments where each particle of a pair traverses a multi-path interferometer. Optimal single-particle interference excludes…

Quantum Physics · Physics 2009-11-10 Dagomir Kaszlikowski , L. C. Kwek , Marek Zukowski , Berthold-Georg Englert

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…

Quantum Physics · Physics 2018-03-06 David Ellerman

We present a sublinear query algorithm for outputting a near-optimal low-rank approximation to any positive semidefinite Toeplitz matrix $T \in \mathbb{R}^{d \times d}$. In particular, for any integer rank $k \leq d$ and $\epsilon,\delta >…

Data Structures and Algorithms · Computer Science 2022-11-22 Michael Kapralov , Hannah Lawrence , Mikhail Makarov , Cameron Musco , Kshiteej Sheth

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…

Optimization and Control · Mathematics 2019-10-22 Tobias Sutter , David Sutter , Peyman Mohajerin Esfahani , John Lygeros

We present an information-theoretic lower bound for the problem of parameter estimation with time-uniform coverage guarantees. Via a new a reduction to sequential testing, we obtain stronger lower bounds that capture the hardness of the…

Information Theory · Computer Science 2024-06-13 John C. Duchi , Saminul Haque

We show that the restricted sharability and distribution of multi-qubit entanglement can be characterized by Tsallis-$q$ entropy. We first provide a class of bipartite entanglement measures named Tsallis-$q$ entanglement, and provide its…

Quantum Physics · Physics 2010-06-30 Jeong San Kim

What is the power of polynomial-time quantum computation with access to an NP oracle? In this work, we focus on two fundamental tasks from the study of Boolean satisfiability (SAT) problems: search-to-decision reductions, and approximate…

Quantum Physics · Physics 2024-09-02 Sevag Gharibian , Jonas Kamminga

In previous work, we presented a novel information-theoretic privacy criterion for query forgery in the domain of information retrieval. Our criterion measured privacy risk as a divergence between the user's and the population's query…

Information Theory · Computer Science 2015-03-19 David Rebollo-Monedero , Javier Parra-Arnau , Jordi Forné

We develop a new framework for establishing approximate factorization of entropy on arbitrary probability spaces, using a geometric notion known as non-negative sectional curvature. The resulting estimates are equivalent to entropy…

Probability · Mathematics 2024-07-29 Pietro Caputo , Justin Salez

Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…

Information Theory · Computer Science 2019-03-26 Philip Chodrow

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…

Computational Complexity · Computer Science 2018-01-16 Alexander A. Sherstov

We study the polynomial-time approximability of the optimal online stochastic bipartite matching algorithm, initiated by Papadimitriou et al. (EC'21). Here, nodes on one side of the graph are given upfront, while at each time $t$, an online…

Data Structures and Algorithms · Computer Science 2024-07-23 Mark Braverman , Mahsa Derakhshan , Tristan Pollner , Amin Saberi , David Wajc
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