Related papers: Mutual R\'enyi information for two disjoint compou…
The amount of mutual information contained in time series of two elements gives a measure of how well their activities are coordinated. In a large, complex network of interacting elements, such as a genetic regulatory network within a cell,…
Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription…
Real-world systems are characterized by complex interactions of their internal degrees of freedom, while living in ever-changing environments whose net effect is to act as additional couplings. Here, we introduce a paradigmatic interacting…
We use mutual information as a measure of the entanglement between 'physical' and thermo-field double degrees of freedom in field theories at finite temperature. We compute this "thermo-mutual information" in simple toy models: a quantum…
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…
The information theoretic quantity known as mutual information finds wide use in classification and community detection analyses to compare two classifications of the same set of objects into groups. In the context of classification…
We consider the problem of decomposing the total mutual information conveyed by a pair of predictor random variables about a target random variable into redundant, unique and synergistic contributions. We focus on the relationship between…
The R\'enyi function plays an important role in the analysis of multifractal random fields. For random fields on the sphere, there are three models in the literature where the R\'enyi function is known explicitly. The theoretical part of…
We identify a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >= I(A:B)+I(A:C), provided…
Mutual information is the reciprocal information that is common to or shared by two or more parties. Quantum mutual information for bipartite quantum systems is non-negative, and bears the interpretation of total correlation between the two…
We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…
We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The…
We prove decomposition rules for quantum R\'enyi mutual information, generalising the relation $I(A:B) = H(A) - H(A|B)$ to inequalities between R\'enyi mutual information and R\'enyi entropy of different orders. The proof uses Beigi's…
Computing entanglement entropy and its cousins is often challenging even in the simplest continuum and lattice models, partly because such entropies depend nontrivially on all geometric characteristics of the entangling region. Quantum…
For spin and fermionic systems in any spatial dimension, we establish that the superpolynomial decay behavior of mutual information and conditional mutual information is a universal property of gapped pure- and mixed-state phases; i.e., all…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
Biochemistry, ecology, and neuroscience are examples of prominent fields aiming at describing interacting systems that exhibit non-trivial couplings to complex, ever-changing environments. We have recently shown that linear interactions and…
The analogues of Arimoto's definition of conditional R\'enyi entropy and R\'enyi mutual information are explored for abstract alphabets. These quantities, although dependent on the reference measure, have some useful properties similar to…
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…
Correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system, widely used in many-body physics and in quantum information science, respectively. We find that…