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Related papers: Swiveled R\'enyi entropies

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The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory.…

Quantum Physics · Physics 2018-07-26 Kaushik P. Seshadreesan , Ludovico Lami , Mark M. Wilde

This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…

Information Theory · Computer Science 2018-12-11 Igal Sason

The Renyi entropy is a generalization of the usual concept of entropy which depends on a parameter q. In fact, Renyi entropy is closely related to free energy. Suppose we start with a system in thermal equilibrium and then suddenly divide…

Quantum Physics · Physics 2022-05-18 John C. Baez

In this paper a new operational definition of Renyi entropy and Renyi divergence is presented. Other operational definitions are mentioned.

Mathematical Physics · Physics 2009-11-11 Peter Harremoes

In a certain sense we generalize the recently introduced and extensively studied notion called quantum R\'enyi divergence (in another name, sandwiched R\'enyi relative entropy) and describe the structures of corresponding symmetries. More…

Functional Analysis · Mathematics 2015-12-09 Marcell Gaál , Lajos Molnár

In this paper the author analyses the weighted Renyi entropy in order to derive several inequalities in weighted case. Furthermore, using the proposed notions $\alpha$-th generalized derivation and ($\alpha$; p)-th weighted Fisher…

Information Theory · Computer Science 2015-10-16 Salimeh Yasaei Sekeh

In quantum mechanics, stringnet condensed states - a family of prototypical states exhibiting non-trivial topological order - can be classified via their long-range entanglement properties, in particular topological corrections to the…

Statistical Mechanics · Physics 2014-05-12 M. Hermanns , S. Trebst

Most quantum divergences derive their structure from classical f-divergences or Renyi-type constructions, a dependence that obscures several quantum geometric effects. We introduce a quantum relative-alpha-entropy that extends Umegaki's…

Quantum Physics · Physics 2026-04-09 Sayantan Roy , Atin Gayen , Aditi Kar Gangopadhyay , Sugata Gangopadhyay

The entropy of probability distribution defined by Shannon has several extensions. R\'enyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum…

Mathematical Physics · Physics 2019-09-04 Farrukh Mukhamedov , Kyouhei Ohmura , Noboru Watanabe

A lower bound on the R\'enyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the…

Information Theory · Computer Science 2015-05-07 Liyao Wang , Mokshay Madiman

I first calculate the charged spherical Renyi entropy by a numerical method that does not require knowledge of any eigenvalue degeneracies, and applies to all odd dimensions. An image method is used to relate the full sphere values to those…

High Energy Physics - Theory · Physics 2016-01-26 J. S. Dowker

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

The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the…

Mathematical Physics · Physics 2023-02-13 Dávid Bugár , Péter Vrana

We consider a two-parameter family of R\'enyi relative entropies $D_{\alpha,z}(\rho||\sigma)$ that are quantum generalisations of the classical R\'enyi divergence $D_{\alpha}(p||q)$. This family includes many known relative entropies (or…

Quantum Physics · Physics 2016-02-23 Koenraad M. R. Audenaert , Nilanjana Datta

The aim of the work is to give the explicit proofs of the Renyi-entropy uncertainty relations presented in the previous work [A. Rastegin, arXiv:0805.1777]. The relations with both the state-dependent and state-independent entropic bounds…

Quantum Physics · Physics 2008-07-18 Alexey E. Rastegin

This paper is twofold. In the first part, we present a refinement of the R\'enyi Entropy Power Inequality (EPI) recently obtained in \cite{BM16}. The proof largely follows the approach in \cite{DCT91} of employing Young's convolution…

Probability · Mathematics 2018-05-01 Jiange Li

The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…

Quantum Physics · Physics 2018-08-13 Mark M. Wilde

We propose a new family of regularized R\'enyi divergences parametrized not only by the order $\alpha$ but also by a variational function space. These new objects are defined by taking the infimal convolution of the standard R\'enyi…

Machine Learning · Statistics 2023-02-16 Jeremiah Birrell , Yannis Pantazis , Paul Dupuis , Markos A. Katsoulakis , Luc Rey-Bellet

We extend previous work on the perturbative expansion of the Renyi entropy, $S_q$, around $q=1$ for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to…

High Energy Physics - Theory · Physics 2015-06-22 Jeongseog Lee , Aitor Lewkowycz , Eric Perlmutter , Benjamin R. Safdi

Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…

Statistical Mechanics · Physics 2019-03-12 Tsung-Cheng Lu , Tarun Grover