Related papers: Mutual R\'enyi information for two disjoint compou…
A new concept of mutual pressure is introduced for potential functions on both continuous and discrete compound spaces via discrete micro-states of permutations, and its relations with the usual pressure and the mutual information are…
Entanglement R\'enyi-$\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement R\'enyi-$\alpha$…
We derive a (2+1)-dimensional multicomponent long-wave$-$short-wave resonance interaction (LSRI) system as the evolution equation for propagation of $N$-dispersive waves in weak Kerr type nonlinear medium in the small amplitude limit. The…
Quantifying cooperation or synergy among random variables in predicting a single target random variable is an important problem in many complex systems. We review three prior information-theoretic measures of synergy and introduce a novel…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
A system's heterogeneity (\textit{diversity}) is the effective size of its event space, and can be quantified using the R\'enyi family of indices (also known as Hill numbers in ecology or Hannah-Kay indices in economics), which are indexed…
By developing a method to represent the Renyi entropies via a replica-trick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi Mutual Information in any Monte Carlo simulation. Through simulations…
Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's…
We define the lower and upper mutual dimensions $mdim(x:y)$ and $Mdim(x:y)$ between any two points $x$ and $y$ in Euclidean space. Intuitively these are the lower and upper densities of the algorithmic information shared by $x$ and $y$. We…
The *reciprocal complement* $R(D)$ of an integral domain $D$ is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of $R(D)$ are determined when $D$ is a polynomial ring in $n\geq 2$…
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…
We show that the separability of states in quantum mechanics has a close counterpart in classical physics, and that conditional mutual information (a.k.a. conditional information transmission) is a very useful quantity in the study of both…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
Mutual information is widely used in artificial intelligence, in a descriptive way, to measure the stochastic dependence of discrete random variables. In order to address questions such as the reliability of the empirical value, one must…
In [Berta et al., J. Math. Phys. 56, 022205 (2015)], we recently proposed Renyi generalizations of the conditional quantum mutual information of a tripartite state on $ABC$ (with $C$ being the conditioning system), which were shown to…
We introduce an innovative and mathematically rigorous definition for computing common information from multi-view data, drawing inspiration from G\'acs-K\"orner common information in information theory. Leveraging this definition, we…
We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions, and are thus the most classical ones among all possible…
Estimating mutual information from observed samples is a basic primitive, useful in several machine learning tasks including correlation mining, information bottleneck clustering, learning a Chow-Liu tree, and conditional independence…
Bivariate Partial Information Decomposition (PID) describes how the mutual information between a random variable M and two random variables Y and Z is decomposed into unique, redundant, and synergistic terms. Recently, PID has shown promise…
Holographic mutual and tripartite information have been studied in a non-conformal background. We have investigated how these observables behave as the energy scale and number of degrees of freedom vary. We have found out that the effect of…