Related papers: Towards Nonadditive Quantum Information Theory
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays the important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of…
The pseudo-additive relation that the Tsallis entropy satisfies has nothing whatsoever to do with the super- and sub- additivity properties of the entropy. The latter properties, like concavity and convexity, are couched in geometric…
Quantum information is about the entanglement of states. To this starting point we add parameters whereby a single state becomes a non-vanishing section of a bundle. We consider through examples the possible entanglement patterns of…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…
This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the…
The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On…
Non Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non Gaussianity of quantum states, based on the…
Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
Within its range of applicability, the Boltzmann equation seems unique in its capacity to accurately describe the transition from almost any initial state to a self-equilibrated thermal state. Using information-theoretic methods to rephrase…
In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum…
In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…
We consider the Shannon-Khinchin axiomatic systems for the characterization of generalized entropies such as Sharma-Mital and Frank-Daffertshofer entropy. We provide the generalization of Shannon-Khinchin axioms and give the corresponding…
The local structure entropy is a new method which is proposed to identify the influential nodes in the complex networks. In this paper a new form of the local structure entropy of the complex networks is proposed based on the Tsallis…
Previous results on Renyi and Wang's formalism of the Tsallis thermostatics are founded by using an extensive variable z connected to the entropic parameter q. It is shown that in the thermodynamical limit both the Tsallis and Renyi…
The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in which…
The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical…
The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari, IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the generalized Shannon-Khinchin's axiom. In the present paper, this result is generalized…
The aim of the paper is to study the link between non additivity of some entropies and their boundedness. We propose an axiomatic construction of the entropy relying on the fact that entropy belongs to a group isomorphic to the usual…