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We introduce a binary relation on the finite discrete probability distributions which generalizes notions of majorization that have been studied in quantum information theory. Motivated by questions in thermodynamics, our relation describes…

Information Theory · Computer Science 2016-04-12 Markus P. Mueller , Michele Pastena

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

Mathematical Physics · Physics 2018-03-02 Alberto Barchielli , Matteo Gregoratti , Alessandro Toigo

This work provides data-processing and majorization inequalities for $f$-divergences, and it considers some of their applications to coding problems. This work also provides tight bounds on the R\'{e}nyi entropy of a function of a discrete…

Information Theory · Computer Science 2021-04-01 Igal Sason

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

In this paper, we introduce novel characterizations of the classical concept of majorization in terms of upper triangular (resp., lower triangular) row-stochastic matrices, and in terms of sequences of linear transforms on vectors. We used…

Information Theory · Computer Science 2024-05-14 Roberto Bruno , Ugo Vaccaro

The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…

Quantum Physics · Physics 2024-09-24 Alexey E. Rastegin

R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…

Information Theory · Computer Science 2010-05-28 Tim van Erven , Peter Harremoës

Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…

Quantum Physics · Physics 2021-06-07 Stefan Floerchinger , Tobias Haas , Ben Hoeber

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

Machine Learning · Computer Science 2024-01-02 Yusuf Sale , Paul Hofman , Lisa Wimmer , Eyke Hüllermeier , Thomas Nagler

The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…

Quantum Physics · Physics 2016-05-16 Gregory A. Howland , James Schneeloch , Daniel J. Lum , John C. Howell

Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…

Quantum Physics · Physics 2026-04-07 Qing-Hua Zhang , Cong Xu , Jing-Feng Wu , Shao-Ming Fei

Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied…

Quantum Physics · Physics 2023-10-30 Carlos de Gois , Kiara Hansenne , Otfried Gühne

Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…

Quantum Physics · Physics 2012-10-18 Marco Tomamichel , Renato Renner

Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…

Quantum Physics · Physics 2018-07-19 Fabricio Toscano , Daniel S. Tasca , Łukasz Rudnicki , Stephen P. Walborn

Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this Letter, we explore this…

Quantum Physics · Physics 2018-07-31 Jun Feng , Yao-Zhong Zhang , Mark D. Gould , Heng Fan

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy…

Information Theory · Computer Science 2013-01-24 Lavanya Sivakumar , Matthias Dehmer

We investigate the additivity properties for both bipartite and multipartite systems by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular,…

Quantum Physics · Physics 2025-02-25 Alberto Riccardi , Giovanni Chesi , Chiara Macchiavello , Lorenzo Maccone

The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a…

Quantum Physics · Physics 2018-02-15 Jun-Li Li , Cong-Feng Qiao

Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…

Quantum Physics · Physics 2013-12-16 Shmuel Friedland , Vlad Gheorghiu , Gilad Gour

Entropic uncertainty relations are powerful tools, especially in quantum cryptography. They typically bound the amount of uncertainty a third-party adversary may hold on a measurement outcome as a result of the measurement overlap. However,…

Quantum Physics · Physics 2023-05-18 Walter O. Krawec