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The Entropy Accumulation Theorem (EAT) was introduced to significantly improve the finite-size rates for device-independent quantum information processing tasks such as device-independent quantum key distribution (QKD). A natural question…

Quantum Physics · Physics 2025-12-17 Ian George , Jie Lin , Thomas van Himbeeck , Kun Fang , Norbert Lütkenhaus

In this work we derive a number of chain rules for mutual information quantities, suitable for analyzing quantum cryptography with imperfect devices that leak additional information to an adversary. First, we derive a chain rule between…

Quantum Physics · Physics 2024-12-10 Amir Arqand , Tony Metger , Ernest Y. -Z. Tan

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…

Statistics Theory · Mathematics 2021-06-18 Abhik Ghosh , Ayanendranath Basu

Security proofs in quantum cryptography rely on conditional entropies. In a many-round protocol, their estimation is a challenging task; one must account for the most general attacks by an eavesdropper, including those that are not…

Quantum Physics · Physics 2026-05-29 Lewis Wooltorton , Peter Brown , Omar Fawzi

We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…

Information Theory · Computer Science 2008-12-18 Jean-François Bercher

Estimating statistical properties is fundamental in statistics and computer science. In this paper, we propose a unified quantum algorithm framework for estimating properties of discrete probability distributions, with estimating R\'enyi…

Quantum Physics · Physics 2024-04-04 Xinzhao Wang , Shengyu Zhang , Tongyang Li

We use a R\'enyi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum or classical communication between two parties. These include state redistribution,…

Quantum Physics · Physics 2016-08-10 Felix Leditzky , Mark M. Wilde , Nilanjana Datta

We introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and…

Machine Learning · Statistics 2023-07-04 Xubo Yue , Raed Kontar

This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$-ary hypothesis testing in terms of the Arimoto-R\'enyi conditional entropy of an arbitrary order $\alpha$. The improved tightness of these bounds over…

Information Theory · Computer Science 2017-12-06 Igal Sason , Sergio Verdú

We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…

Quantum Physics · Physics 2014-02-19 F. Dupuis , L. Kraemer , P. Faist , J. M. Renes , R. Renner

The rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum…

Quantum Physics · Physics 2022-10-05 Peter Brown , Hamza Fawzi , Omar Fawzi

Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…

Quantum Physics · Physics 2025-12-23 Adam Brandenburger , Pierfrancesco La Mura

A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…

Information Theory · Computer Science 2015-10-20 Igal Sason , Sergio Verdu

Recently, information theoretic analysis has become a popular framework for understanding the generalization behavior of deep neural networks. It allows a direct analysis for stochastic gradient/Langevin descent (SGD/SGLD) learning…

Machine Learning · Statistics 2023-05-03 Yuxin Dong , Tieliang Gong , Hong Chen , Chen Li

A realistic Quantum Key Distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem…

Quantum Physics · Physics 2011-10-13 Silvestre Abruzzo , Hermann Kampermann , Markus Mertz , Dagmar Bruß

Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset of a string, given a bound on the min-entropy of the whole string. K\"onig and Renner showed a min-entropy sampling theorem that holds relative to quantum…

Quantum Physics · Physics 2011-07-18 Jürg Wullschleger

Entanglement R\'enyi-$\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement R\'enyi-$\alpha$…

Quantum Physics · Physics 2017-03-07 Wei Song , Lin Chen , Zhuo-Liang Cao

We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic…

Quantum Physics · Physics 2022-10-05 Frederic Dupuis , Omar Fawzi , Renato Renner

Device-independent (DI) cryptography represents the highest level of security, enabling cryptographic primitives to be executed safely on uncharacterized devices. Moreover, with successful proof-of-concept demonstrations in randomness…

Quantum Physics · Physics 2025-07-11 Thomas A. Hahn , Aby Philip , Ernest Y. -Z. Tan , Peter Brown

We introduce an improved one-shot characterisation of randomness extraction against quantum side information (privacy amplification), strengthening known one-shot bounds and providing a unified derivation of the tightest known asymptotic…

Quantum Physics · Physics 2026-04-07 Bartosz Regula , Marco Tomamichel