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Related papers: Estimates for Tsallis relative operator entropy

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In this paper, we study entropic uncertainty relations on a finite-dimensional Hilbert space and provide several tighter bounds for multi-measurements, with some of them also valid for R\'{e}nyi and Tsallis entropies besides the Shannon…

Quantum Physics · Physics 2016-05-02 Yunlong Xiao , Naihuan Jing , Shao-Ming Fei , Tao Li , Xianqing Li-Jost , Teng Ma , Zhi-Xi Wang

We shall show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that the Tsallis entropy function is characterized by a functional equation, which is a…

Information Theory · Computer Science 2010-05-20 Shigeru Furuichi

We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order $q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for $q=2$ or $3$.…

Quantum Physics · Physics 2016-12-15 Jeong San Kim

The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…

Statistical Mechanics · Physics 2007-05-23 Qiuping A. Wang

A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-maxwellian distributions obtained from the Boltzmann-Gibbs entropy is afforded.

Quantum Physics · Physics 2009-11-13 N. G. de Almeida

We present unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Poly\'a and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp…

Functional Analysis · Mathematics 2022-01-19 Vladislav Babenko , Yuliya Babenko , Nadiia Kriachko , Dmytro Skorokhodov

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction…

Functional Analysis · Mathematics 2022-07-08 K. P. Deepesh , V. B. Kiran Kumar

We study Rellich inequalities associated to higher-order elliptic operators in the Euclidean space. The inequalities are expressed in terms of an associated Finsler metric. In the case of half-spaces we obtain the sharp constant while for a…

Analysis of PDEs · Mathematics 2021-08-06 Gerassimos Barbatis , Miltiadis Paschalis

In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to…

Functional Analysis · Mathematics 2014-06-24 Nacib Albuquerque , Frédéric Bayart , Daniel Pellegrino , Juan B. Seoane-Sepúlveda

For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…

Optimization and Control · Mathematics 2022-12-13 Fritz Colonius , Boumediene Hamzi

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the $H^2$ and $H^{\infty}$ norms of functions in model spaces.

Functional Analysis · Mathematics 2009-07-20 Stephan Ramon Garcia , William T. Ross

Functional version for the so-called Furuta parametric relative operator entropy is here investigated. Some related functional inequalities are also discussed. The theoretical results obtained by our functional approach immediately imply…

Functional Analysis · Mathematics 2018-03-30 Mustapha Raïssouli , Shigeru Furuichi

In this paper the complete solution of the restricted inequalities for supremal operators are given. The boundedness of the composition of supremal operators with the Hardy and Copson operators in weighted Lebesgue spaces are characterized.

Functional Analysis · Mathematics 2020-02-05 Amiran Gogatishvili , Rza Mustafayev

Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…

Statistical Mechanics · Physics 2007-05-23 Franck Jedrzejewski

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

Functional Analysis · Mathematics 2007-05-23 Sever Silvestru Dragomir

We review some results and proofs on eigenvalue bounds for random Schr\"odinger operators with complex-valued potentials. We also include new Schatten norm estimates for the resolvent and use them to obtain bounds for sums of eigenvalues.

Spectral Theory · Mathematics 2023-08-29 Jean-Claude Cuenin , Konstantin Merz

In this short report, we give some new entropy inequalities based on R\'{e}nyi relative entropy and the observation made by Berta {\em et al} [arXiv:1403.6102]. These inequalities obtained extends some well-known entropy inequalities. We…

Quantum Physics · Physics 2014-04-16 Lin Zhang

We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.

Functional Analysis · Mathematics 2016-10-14 Nabil Machrafi , Aziz Elbour , Mohammed Moussa

We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the…

Statistical Mechanics · Physics 2015-05-14 Hideo Hasegawa

It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.

Statistical Mechanics · Physics 2009-11-10 Andrei G. Bashkirov