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One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence and information spectrum divergence, that characterize various operational tasks and are used to…

Quantum Physics · Physics 2020-08-24 Anurag Anshu , Mario Berta , Rahul Jain , Marco Tomamichel

In this work, we provide a strengthening of the data processing inequality for the relative entropy introduced by Belavkin and Staszewski (BS-entropy). This extends previous results by Carlen and Vershynina for the relative entropy and…

Mathematical Physics · Physics 2020-03-13 Andreas Bluhm , Angela Capel

Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…

Quantum Physics · Physics 2025-05-21 Matheus Capela , Kaumudibikash Goswami

We prove an achievability result for privacy amplification and decoupling in terms of the sandwiched R\'enyi entropy of order $\alpha \in (1,2]$; this extends previous results which worked for $\alpha=2$. The fact that this proof works for…

Quantum Physics · Physics 2022-01-11 Frédéric Dupuis

We introduce a set of useful expressions of Differential Privacy (DP) notions in terms of the Laplace transform of the privacy loss distribution. Its bare form expression appears in several related works on analyzing DP, either as an…

Machine Learning · Computer Science 2024-11-15 Rishav Chourasia , Uzair Javaid , Biplap Sikdar

We study the Hoeffding regime of composite quantum hypothesis testing, in which each hypothesis is specified by a sequence of sets of quantum states. We establish quantum Hoeffding bounds under a set of structural assumptions, orthogonal to…

Quantum Physics · Physics 2026-05-05 Masahito Hayashi , Kun Fang

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's…

Quantum Physics · Physics 2015-12-31 Nilanjana Datta , Tony Dorlas , Richard Jozsa , Fabio Benatti

Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor…

Machine Learning · Computer Science 2014-06-06 Onur Dikmen , Zhirong Yang , Erkki Oja

Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…

Information Theory · Computer Science 2025-04-23 Aaron J. Gutknecht , Fernando E. Rosas , David A. Ehrlich , Abdullah Makkeh , Pedro A. M. Mediano , Michael Wibral

We show that Araki and Masuda's weighted non-commutative vector valued $L_p$-spaces [Araki \& Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)] correspond to an algebraic generalization of the sandwiched R\'enyi divergences with parameter…

Mathematical Physics · Physics 2018-12-12 Mario Berta , Volkher B. Scholz , Marco Tomamichel

We explore the role of sandwiched Renyi relative entropy in AdS/CFT and in finite-dimensional models of holographic quantum error correction. In particular, in the context of operator algebra quantum error correction, we discuss a suitable…

High Energy Physics - Theory · Physics 2022-04-19 Reginald J. Caginalp

There are different inequivalent ways to define the R\'enyi capacity of a channel for a fixed input distribution $P$. In a 1995 paper Csisz\'ar has shown that for classical discrete memoryless channels there is a distinguished such quantity…

Quantum Physics · Physics 2023-01-18 Milán Mosonyi , Tomohiro Ogawa

This is a survey paper with some original results of the author on refined versions of the Azuma-Hoeffding inequality with some examples that are related to information theory. This work has evolved to the joint paper with Maxim Raginsky in…

Information Theory · Computer Science 2013-03-14 Igal Sason

We determine the quantum states and measurements that optimize the accessible information in a reference frame alignment protocol associated with the groups U(1), corresponding to a phase reference, and $\mathbb{Z}_M$, the cyclic group of…

Quantum Physics · Physics 2012-07-17 Michael Skotiniotis , Gilad Gour

We prove decomposition rules for quantum R\'enyi mutual information, generalising the relation $I(A:B) = H(A) - H(A|B)$ to inequalities between R\'enyi mutual information and R\'enyi entropy of different orders. The proof uses Beigi's…

Quantum Physics · Physics 2020-07-23 Alexander McKinlay , Marco Tomamichel

We derive the information geometry induced by the statistical R\'enyi divergence, namely its metric tensor, its dual parametrized connections, as well as its dual Laplacians. Based on these results, we demonstrate that the R\'enyi-geometry,…

Statistics Theory · Mathematics 2025-06-17 Rebecca Maria Kuntz , Heinrich von Campe , Björn Malte Schäfer

Sparse high-dimensional linear regression is a central problem in statistics, where the goal is often variable selection and/or coefficient estimation. We propose a mean-field variational Bayes approximation for sparse regression with…

Methodology · Statistics 2025-12-02 Chadi Bsila , Yiqi Tang , Kaiwen Wang , Laurie Heyer

The fidelity-based smooth min-relative entropy is a distinguishability measure that has appeared in a variety of contexts in prior work on quantum information, including resource theories like thermodynamics and coherence. Here we provide a…

Quantum Physics · Physics 2024-05-29 Theshani Nuradha , Mark M. Wilde

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

The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an…

Quantum Physics · Physics 2013-08-14 Michael Zwolak , Wojciech H. Zurek
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