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We study the behavior of the R\'enyi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that R\'enyi entropies of different index…

Quantum Physics · Physics 2013-05-31 Alioscia Hamma , Lukasz Cincio , Siddhartha Santra , Paolo Zanardi , Luigi Amico

It has been known for a long time that the mutual information between the input sequence and output of a binary symmetric channel (BSC) is upper bounded by the mutual information between the same input sequence and the output of a binary…

Information Theory · Computer Science 2024-01-29 Uri Erez , Or Ordentlich , Shlomo Shamai

Quantum key distribution requires tight and reliable bounds on the secret key rate to ensure robust security. This is particularly so for the regime of finite block sizes, where the optimization of generalized R\'enyi entropic quantities is…

Quantum Physics · Physics 2026-04-09 Rebecca R. B. Chung , Nelly H. Y. Ng , Yu Cai

The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…

Mathematical Physics · Physics 2016-09-26 Hadi Reisizadeh , S. Mahmoud Manjegani

The problem of how to properly quantify redundant information is an open question that has been the subject of much recent research. Redundant information refers to information about a target variable S that is common to two or more…

Information Theory · Computer Science 2017-07-14 Robin A. A. Ince

We develop a general theory for computing the Renyi entropy with general multiple disjoint intervals from the swapping operations. Our theory is proposed based on the fact that we have observed the resemblance between the replica trick in…

Statistical Mechanics · Physics 2026-04-03 Han-Qing Shi , Hai-Qing Zhang

Universal hash functions map the output of a source to random strings over a finite alphabet, aiming to approximate the uniform distribution on the set of strings. A classic result on these functions, called the Leftover Hash Lemma, gives…

Information Theory · Computer Science 2026-01-05 Madhura Pathegama , Alexander Barg

We obtain two new additivity results of quantum channels. The first one is the additivity of the channel R\'enyi information associated with the sandwiched R\'enyi divergence of order $\alpha\in[\frac{1}{2},1)$. To prove this, we introduce…

Quantum Physics · Physics 2026-03-18 Ke Li , Quanhua Xu

R\'enyi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of R\'enyi…

Mathematical Physics · Physics 2021-06-29 Debraj Nath

Using the density matrix renormalization group, we investigate the Renyi entropy of the anisotropic spin-s Heisenberg chains in a z-magnetic field. We considered the half-odd integer spin-s chains, with s=1/2,3/2 and 5/2, and periodic and…

Statistical Mechanics · Physics 2015-05-27 J. C. Xavier , F. C. Alcaraz

Conventional information-theoretic quantities assume access to probability distributions. Estimating such distributions is not trivial. Here, we consider function-based formulations of cross entropy that sidesteps this a priori estimation…

Information Theory · Computer Science 2021-09-27 Isaac J. Sledge , Jose C. Principe

Entanglement criteria for an $n$-partite quantum system with continuous variables are formulated in terms of R\'{e}nyi entropies. R\'{e}nyi entropies are widely used as a good information measure due to many nice properties. Derived…

Quantum Physics · Physics 2017-05-22 Alexey E. Rastegin

The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…

Statistics Theory · Mathematics 2013-03-08 David Källberg , Nikolaj Leonenko , Oleg Seleznjev

One way to diagnose chaos in bipartite unitary channels is via the tripartite information of the corresponding Choi state, which for certain choices of the subsystems reduces to the negative conditional mutual information (CMI). We study…

Quantum Physics · Physics 2017-01-25 Dawei Ding , Patrick Hayden , Michael Walter

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

We introduce a biparametric Fisher-R\'enyi complexity measure for general probability distributions and we discuss its properties. This notion, which is composed of two entropy-like components (the R\'enyi entropy and the biparametric…

Quantum Physics · Physics 2017-11-16 D. Puertas-Centeno , I. V. Toranzo , J. S. Dehesa

We study the Shannon mutual information in one-dimensional critical spin chains, following a recent conjecture (Phys. Rev. Lett. 111, 017201 (2013)), as well as R\'enyi generalizations of it. We combine conformal field theory arguments with…

Statistical Mechanics · Physics 2014-08-04 Jean-Marie Stéphan

We investigate the analogy between the renormalization group (RG) and deep neural networks, wherein subsequent layers of neurons are analogous to successive steps along the RG. In particular, we quantify the flow of information by…

High Energy Physics - Theory · Physics 2021-12-22 Johanna Erdmenger , Kevin T. Grosvenor , Ro Jefferson

We establish a correspondence between two independent entropic probes -- the variation of R\'{e}nyi mutual information (RMI) across the electroweak symmetry breaking (EWSB) transition and the stabilizer R\'enyi entropy (SRE) -- in…

High Energy Physics - Phenomenology · Physics 2026-05-22 Qing-Hong Cao , Yandong Liu , Haotian Qi , Hao Zhang , Haoran Zhao

The $\alpha$-sandwiched R\'enyi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\alpha\geq 1/2$. In this article, we derive a necessary and sufficient algebraic condition for equality in…

Quantum Physics · Physics 2017-12-15 Felix Leditzky , Cambyse Rouzé , Nilanjana Datta