Related papers: Conditional Information Inequalities for Entropic …
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…
A direct connection of information entropy $S$ and kinetic energy $T$ is obtained for nuclei and atomic clusters, which establishes $T$ as a measure of the information in a distribution. It is conjectured that this is a universal property…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…
The challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states (density operators). A…
In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
This paper studies the informativity problem for reachability and null-controllability of constrained systems. To be precise, we will focus on an unknown linear systems with convex conic constraints from which we measure data consisting of…
The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy, and a complete proof of the uniqueness theorem for the…
The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here we consider the chain rule for the more general smooth…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
We propose a generalization of the asymptotic equipartition property to discrete sources with an ambiguous alphabet, and prove that it holds for irreducible stationary Markov sources with an arbitrary distinguishability relation. Our…
The assumption of local realism in a Bell locality scenario imposes non-trivial conditions on the Shannon entropies of the associated probability distributions, expressed by linear entropic Bell inequalities. In principle, these entropic…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
The derivation of Bell inequalities in terms of quantum statistical (thermodynamic) entropies is considered. Inequalities of the Wigner form are derived but shown to be extremely limiting in their applicability due to the nature of the…
Although compartmental dynamical systems are used in many different areas of science, model selection based on the maximum entropy principle (MaxEnt) is challenging because of the lack of methods for quantifying the entropy for this type of…
We show that a proper expression of the uncertainty relation for a pair of canonically-conjugate continuous variables relies on entropy power, a standard notion in Shannon information theory for real-valued signals. The resulting…
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as…