Related papers: On bounds of Tsallis relative entropy and an inequ…
Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies, such as quantum computation, quantum communication and quantum metrology. Yet, their quantification, rather than…
We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This…
The fractal and self-similarity properties are revealed in many complex networks. In order to show the influence of different part in the complex networks to the information dimension, we have proposed a new information dimension based on…
In this paper, we aim to replace in the definitions of covariance and correlation the usual trace {\rm Tr} by a tracial positive map between unital $C^*$-algebras and to replace the functions $x^{\alpha}$ and $x^{1-\alpha}$ by functions $f$…
We study the fundamental properties of the quantum f-relative entropy, where f(.) is an operator convex function. We give the equality conditions under monotonicity and joint convexity, and these conditions are more general than, since they…
How complex of the complex networks has attracted many researchers to explore it. The entropy is an useful method to describe the degree of the $complex$ of the complex networks. In this paper, a new method which is based on the Tsallis…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very…
We discuss the notion of hidden correlations in classical and quantum indivisible systems along with such characteristics of the correlations as the mutual information and conditional information corresponding to the entropic subadditivity…
The problem of quantum state inference and the concept of quantum entanglement are studied using a non-additive measure in the form of Tsallis entropy indexed by the positive parameter q. The maximum entropy principle associated with this…
We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence $S(x)$. We establish recurrence…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
Fidelity is a fundamental and ubiquitous concept in quantum information theory. Fuchs-van de Graaf's inequalities deal with bounding fidelity from above and below. In this paper, we give a lower bound on the quantum fidelity between two…
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting…
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
It is well known that loss of information about a system, for some observer, leads to an increase in entropy as perceived by this observer. We use this to propose an alternative approach to decoherence in quantum field theory in which the…
We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second…
One of the major achievements of the recently emerged quantum information theory is the introduction and thorough investigation of the notion of quantum channel which is a basic building block of any data-transmitting or data-processing…