Related papers: A Logarithmic Decomposition for Information
Learning-based lossy image compression usually involves the joint optimization of rate-distortion performance. Most existing methods adopt spatially invariant bit length allocation and incorporate discrete entropy approximation to constrain…
Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this…
We study formal properties of smooth max-information, a generalization of von Neumann mutual information derived from the max-relative entropy. Recent work suggests that it is a useful quantity in one-shot channel coding, quantum rate…
Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a…
Shannon entropy ($S$), R{\'e}nyi entropy ($R$), Tsallis entropy ($T$), Fisher information ($I$) and Onicescu energy ($E$) have been explored extensively in both \emph{free} H atom (FHA) and \emph{confined} H atom (CHA). For a given quantum…
Accurately matching visual and textual data in cross-modal retrieval has been widely studied in the multimedia community. To address these challenges posited by the heterogeneity gap and the semantic gap, we propose integrating Shannon…
We study the universal behavior of quantum information-theoretic quantities in thermalized isolated quantum many-body systems and evaporating black holes. In particular, we study a genuine mixed-state entanglement measure called the…
Given any finite set equipped with a probability measure, one may compute its Shannon entropy or information content. The entropy becomes the logarithm of the cardinality of the set when the uniform probability is used. Leinster introduced…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
Information has an entropic character which can be analyzed within the Statistical Theory in molecular systems. R. Landauer and C.H. Bennett showed that a logical copy can be carried out in the limit of no dissipation if the computation is…
We present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity…
We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. This framework enables us to express an indirect…
Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible $N$--point correlation is measured by a decrease…
In recent years, there has been an upswing of interest in estimating information from data emerging in a lot of areas beyond communications. This paper aims at estimating the information between two random phenomena by using consolidated…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Position and momentum information measures are evaluated for the ground state of the \emph{relativistic} hydrogen-like atoms. Consequences of the fact that the radial momentum operator is not self-adjoint are explicitly studied, exhibiting…
The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…