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The simplest example of a quantum information source with memory is a mixed source which emits signals entirely from one of two memoryless quantum sources with given a priori probabilities. Considering a mixed source consisting of a general…

Quantum Physics · Physics 2016-06-27 Felix Leditzky , Nilanjana Datta

Given an independent and identically distributed source $X = \{X_i \}_{i=1}^{\infty}$ with finite Shannon entropy or differential entropy (as the case may be) $H(X)$, the non-asymptotic equipartition property (NEP) with respect to $H(X)$ is…

Information Theory · Computer Science 2012-04-18 En-Hui Yang , Jin Meng

This paper considers the joint compression of a pair of correlated sources, where the encoder is allowed to access only one of the sources. The objective is to recover both sources under separate distortion constraints for each source while…

Information Theory · Computer Science 2024-11-07 Huiyuan Yang , Yuxuan Shi , Shuo Shao , Xiaojun Yuan

We study channel simulation under common randomness assistance in the finite-blocklength regime and identify the smooth channel max-information as a linear program one-shot converse on the minimal simulation cost for fixed error tolerance.…

Information Theory · Computer Science 2024-10-10 Michael X. Cao , Navneeth Ramakrishnan , Mario Berta , Marco Tomamichel

We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In an article by Grubisic and…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Hans Ringstrom

Bounds on information combining are a fundamental tool in coding theory, in particular when analyzing polar codes and belief propagation. They usually bound the evolution of random variables with respect to their Shannon entropy. In recent…

Information Theory · Computer Science 2023-05-05 Christoph Hirche , Xinyue Guan , Marco Tomamichel

Dimension is an inherent bottleneck to some modern learning tasks, where optimization methods suffer from the size of the data. In this paper, we study non-isotropic distributions of data and develop tools that aim at reducing these…

Machine Learning · Statistics 2025-02-12 Mathieu Even , Laurent Massoulié

An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix $\beta$-ensembles. The conditioning is that…

Mathematical Physics · Physics 2015-05-30 Peter J. Forrester , Nicholas S. Witte

Recently, the present authors derived new asymptotic expansions for linear differential equations having a simple turning point. These involve Airy functions and slowly varying coefficient functions, and were simpler than previous…

Classical Analysis and ODEs · Mathematics 2020-04-28 T. M. Dunster , A. Gil , J. Segura

We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only…

Quantum Physics · Physics 2025-08-12 Milán Mosonyi , Gergely Bunth , Péter Vrana

In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found…

Classical Analysis and ODEs · Mathematics 2017-07-07 Gergő Nemes

We study the problem of solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms. We devise a novel algorithm, referred to as Recursive One-Over-T SGD (ROOT-SGD), based on an easily…

Optimization and Control · Mathematics 2024-09-19 Chris Junchi Li , Wenlong Mou , Martin J. Wainwright , Michael I. Jordan

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

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

The Ryu-Takayanagi (RT) formula and its interpretation in terms of quantum error correction (QEC) implies an emergent locality for the spread of quantum information in holographic CFTs, where information injected at a point in the boundary…

High Energy Physics - Theory · Physics 2026-05-05 Jatin Narde , Onkar Parrikar , Harshit Rajgadia , Sandip Trivedi

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the…

Quantum Physics · Physics 2015-12-02 Mario Berta , Fabian Furrer , Volkher B. Scholz

We show that the R\'enyi entropies of single particle, extended wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the R\'enyi entropy, $S_{n}$, where $|n|<1$, it is…

Mesoscale and Nanoscale Physics · Physics 2013-02-04 Xiao Chen , Benjamin Hsu , Taylor L. Hughes , Eduardo Fradkin

This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and…

Information Theory · Computer Science 2024-08-20 Huiyuan Yang , Yuxuan Shi , Shuo Shao , Xiaojun Yuan

In their recent paper [Phys. Rev. E 99 (2019) 032134], T. Oikinomou and B. Bagci have argued that R\'enyi entropy is ill-suited for inference purposes because it is not consistent with the Shore{ Johnson axioms of statistical estimation…

Data Analysis, Statistics and Probability · Physics 2019-08-27 Petr Jizba , Jan Korbel

Let $\{X_i\}_{i=-\infty}^{\infty}$ be a sequence of random vectors and $Y_{in}=f_{in}(\mathcal{X}_{i,\ell})$ be zero mean block-variables where $\mathcal{X}_{i,\ell}=(X_i,...,X_{i+\ell-1}),i\geq 1$, are overlapping blocks of length $\ell$…

Statistics Theory · Mathematics 2007-08-22 S. N. Lahiri
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