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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

Subword tokenization is a key part of many NLP pipelines. However, little is known about why some tokenizer and hyperparameter combinations lead to better downstream model performance than others. We propose that good tokenizers lead to…

Computation and Language · Computer Science 2023-06-30 Vilém Zouhar , Clara Meister , Juan Luis Gastaldi , Li Du , Mrinmaya Sachan , Ryan Cotterell

We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…

Quantum Physics · Physics 2024-11-20 Simon Becker , Nilanjana Datta , Michael G. Jabbour

We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a…

Information Theory · Computer Science 2015-09-23 Varun Jog , Po-Ling Loh

The information content of a source is defined in terms of the minimum number of bits needed to store the output of the source in a perfectly recoverable way. A similar definition can be given in the case of quantum sources, with qubits…

Quantum Physics · Physics 2023-04-03 Paolo Perinotti , Alessandro Tosini , Leonardo Vaglini

We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of…

Probability · Mathematics 2008-10-06 Oliver Johnson

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

The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate…

Statistical Mechanics · Physics 2017-11-10 Anthony J. Wood , Richard A. Blythe , Martin R. Evans

The conditional quantum mutual information $I(A;B|C)$ of a tripartite state $\rho_{ABC}$ is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is…

Quantum Physics · Physics 2015-03-17 Mario Berta , Kaushik P. Seshadreesan , Mark M. Wilde

An information theoretic approach to bounds in superconformal field theories is proposed. It is proved that the supersymmetric R\'enyi entropy $\bar S_\alpha$ is a monotonically decreasing function of $\alpha$ and $(\alpha-1)\bar S_\alpha$…

High Energy Physics - Theory · Physics 2023-03-03 Yang Zhou

This paper provides upper and lower bounds on the optimal guessing moments of a random variable taking values on a finite set when side information may be available. These moments quantify the number of guesses required for correctly…

Information Theory · Computer Science 2018-06-22 Igal Sason , Sergio Verdú

Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…

High Energy Physics - Theory · Physics 2014-12-12 Nima Lashkari

We compute the entanglement entropy in a 2+1 dimensional topological order in the presence of gapped boundaries. Specifically, we consider entanglement cuts that cut through the boundaries. We argue that based on general considerations of…

High Energy Physics - Theory · Physics 2020-01-08 Ce Shen , Jiaqi Lou , Ling-Yan Hung

We discuss the Renyi entanglement entropies of descendant states in critical one-dimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory…

Statistical Mechanics · Physics 2016-09-27 Luca Taddia , Fabio Ortolani , Tamás Pálmai

The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…

Statistical Mechanics · Physics 2015-05-13 Christian Beck

We investigate the universal inequalities relating the alpha-Renyi entropies of the marginals of a multi-partite quantum state. This is in analogy to the same question for the Shannon and von Neumann entropy (alpha=1) which are known to…

Quantum Physics · Physics 2013-12-24 Noah Linden , Milán Mosonyi , Andreas Winter

Recently a new quantum generalization of the Renyi divergence and the corresponding conditional Renyi entropies was proposed. Here we report on a surprising relation between conditional Renyi entropies based on this new generalization and…

Quantum Physics · Physics 2014-08-18 Marco Tomamichel , Mario Berta , Masahito Hayashi

Entropy is one of the central quantities in thermodynamics, whose flow between two systems determines the statistics of energy transfers. In quantum systems entropy is non-linear in density matrix whose time evolution is cumbersome. Using…

Mesoscale and Nanoscale Physics · Physics 2019-12-06 Mohammad H. Ansari

In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…

Quantum Physics · Physics 2018-10-25 Christian Majenz

In recent years, the Renyi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Renyi entropy is studied. A compact general formula is presented for the lower…

Quantum Physics · Physics 2016-08-05 Sumiyoshi Abe