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This paper systematically develops the resource theory of asymmetric distinguishability, as initiated roughly a decade ago [K. Matsumoto, arXiv:1010.1030 (2010)]. The key constituents of this resource theory are quantum boxes, consisting of…

Quantum Physics · Physics 2019-12-18 Xin Wang , Mark M. Wilde

Neural-network-based compressors have proven to be remarkably effective at compressing sources, such as images, that are nominally high-dimensional but presumed to be concentrated on a low-dimensional manifold. We consider a continuous-time…

Information Theory · Computer Science 2020-11-11 Aaron B. Wagner , Johannes Ballé

The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs,…

Information Theory · Computer Science 2020-07-15 Lampros Gavalakis , Ioannis Kontoyiannis

The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size…

Quantum Physics · Physics 2025-12-22 Amir Arqand , Thomas A. Hahn , Ernest Y. -Z. Tan

We investigated the asymptotics of high-rate constrained quantization errors for a compactly supported probability measure P on Euclidean spaces whose quantizers are confined to a closed set S. The key tool is the metric projection of K…

Metric Geometry · Mathematics 2025-05-19 Chenxing Qian

We study beyond worst-case dimensionality reduction for $s$-sparse vectors. Our work is divided into two parts, each focusing on a different facet of beyond worst-case analysis: We first consider average-case guarantees. A folklore upper…

Data Structures and Algorithms · Computer Science 2025-02-28 Sandeep Silwal , David P. Woodruff , Qiuyi Zhang

Minimum power required to achieve a distortion-noise profile, i.e., a function indicating the maximum allowed distortion value for each noise level, is studied for the transmission of Gaussian sources over Gaussian channels under a regime…

Information Theory · Computer Science 2020-01-22 Mohammadamin Baniasadi , Ertem Tuncel

In the communication problem $\mathbf{UR}$ (universal relation) [KRW95], Alice and Bob respectively receive $x$ and $y$ in $\{0,1\}^n$ with the promise that $x\neq y$. The last player to receive a message must output an index $i$ such that…

Computational Complexity · Computer Science 2017-03-24 Jelani Nelson , Jakub Pachocki , Zhengyu Wang

We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to…

Quantum Physics · Physics 2016-09-08 Andreas Winter

Consider a lossy compression system with $\ell$ distributed encoders and a centralized decoder. Each encoder compresses its observed source and forwards the compressed data to the decoder for joint reconstruction of the target signals under…

Information Theory · Computer Science 2018-07-19 Yizhong Wang , Li Xie , Xuan Zhang , Jun Chen

We prove that for any infinite-dimensional quantum channel the entropic disturbance (defined as difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel) is lower…

Quantum Physics · Physics 2018-01-17 M. E. Shirokov , A. S. Holevo

We are concerned with spherically symmetric solutions to the Euler equations for the multi-dimensional compressible fluids, which have many applications in diverse real physical situations. The system can be reduced to one dimensional…

Analysis of PDEs · Mathematics 2019-08-20 Feimin Huang , Tianhong Li , Difan Yuan

This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…

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

We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…

Quantum Physics · Physics 2019-10-18 Simon Morelli , Claude Klöckl , Christopher Eltschka , Jens Siewert , Marcus Huber

We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) method. In contrast to BC, which uses…

This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…

Probability · Mathematics 2024-06-06 Alberto Gonzalez-Sanz , Jean-Michel Loubes , Jonathan Niles-Weed

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…

Quantum Physics · Physics 2018-10-25 Christian Majenz

A lossy source code $\mathcal{C}$ with rate $R$ for a discrete memoryless source $S$ is called subset-universal if for every $0<R'< R$, almost every subset of $2^{nR'}$ of its codewords achieves average distortion close to the source's…

Information Theory · Computer Science 2015-03-13 Or Ordentlich , Ofer Shayevitz

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…

Quantum Physics · Physics 2016-09-06 Andreas Winter

The variance of (relative) surprisal, also known as varentropy, so far mostly plays a role in information theory as quantifying the leading order corrections to asymptotic i.i.d.~limits. Here, we comprehensively study the use of it to…

Quantum Physics · Physics 2022-03-30 Paul Boes , Nelly H. Y. Ng , Henrik Wilming