Related papers: Derivation of density operators for generalized en…
We show that if one uses the invariant form of the Boltzmann-Shannon continuous entropy, it is possible to obtain the generalized Pareto-Tsallis density function, using an appropriate "prior" measure m_{q}(x) and a "Boltzman constraint"…
Estimating vibrational entropy is a significant challenge in thermodynamics and statistical mechanics due to its reliance on quantum mechanical properties. This paper introduces a quantum algorithm designed to estimate vibrational entropy…
This article is a continuation of my paper [arxiv: 1409.1015v2]. R\'enyi and Tsallis entropies are associated to positive linear operators and properties of some functions related to these entropies are investigated.
We describe a quantum algorithm to estimate the $\alpha$-Renyi entropy of an unknown density matrix $\rho\in\mathcal{C}^{d\times d}$ for $\alpha\neq 1$ by combining the recent technique of quantum singular value transformations with the…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…
The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by the use of Hermite-Hadamard inequality. Thus, we obtain alternative bounds for the Tsallis relative operator entropy. In the process to…
The aim of the present paper is to present a careful and accessible discussion of the formal aspects of Boltzmann-Gibbs and Tsallis entropies. We begin with a brief overview of Boltzmann-Gibbs entropy, highlighting its main properties and…
The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper we investigate these notions putting an emphasis on the geometrical…
The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy…
The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
We analyze the relationships between game theory and quantum mechanics and the extensions to statistical physics and information theory. We use certain quantization relationships to assign quantum states to the strategies of a player. These…
The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator $A$ in a Hilbert space. Using the quantum…
Analytically continuing the von Neumann entropy from R\'enyi entropies is a challenging task in quantum field theory. While the $n$-th R\'enyi entropy can be computed using the replica method in the path integral representation of quantum…
We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator {\rho}, tr {\rho}=1. Let I(P)\in R be defined for any partition P =…
Entanglement is the fundamental quantum property behind the now popular field of quantum transport of information. This quantum property is incompatible with the separation of a single system into two uncorrelated subsystems. Consequently,…
Quantum Information is a new area of research which has been growing rapidly since the last decade. This topic is very close to potential applications to the so called Quantum Computer. In our point of view it makes sense to develop a more…
The macroscopic hydrodynamic equations are derived for many-body systems in the local-equilibrium approach, using the Schr\"odinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic…
We construct the number operator for particles obeying infinite statistics, defined by a generalized q-deformation of the Heisenberg algebra, and prove the positivity of the norm of linearly independent state vectors.
In this article we examine the densities of a product and a ratio of two real positive scalar random variables $x_1$ and $x_2$, which are statistically independently distributed, and we consider the density of the product $u_1=x_1x_2$ as…