Related papers: Measurements and Information in Spin Foam Models
New entropic inequality for quantum and tomographic Shannon information for system of two qubits is obtained. The inequality relating quantum information and spin-tomographic information for particle with spin j = 3=2 is found. The method…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…
We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang…
This paper is prepared as a contribution to the proceedings after the 12th ICSSUR/Feynfest Conference held in Foz do Iguacu (Brazil) from 2 to 6 May 2011. In the first part I briefy report the topic of entropic uncertainty relations for…
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…
The concept of Shannon entropy of random variables was generalized to measurable functions in general, and to simple functions with finite values in particular. It is shown that the information measure of a function is related to the time…
We normalize the combinatorial Laplacian of a graph by the degree sum, look at its eigenvalues as a probability distribution and then study its Shannon entropy. Equivalently, we represent a graph with a quantum mechanical state and study…
Spin foams are candidate state-sum models for transition amplitudes in quantum gravity. An active research subject is to identify the possible divergences of spin foam models, or alternatively to show that models are finite. We will discuss…
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…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
The so-called Darboux III oscillator is an exactly solvable $N$-dimensional nonlinear oscillator defined on a radially symmetric space with non-constant negative curvature. This oscillator can be interpreted as a smooth (super)integrable…
I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are introduced (following hep-th/0205268) to deal…
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and…
We describe a class of spin foam models of four-dimensional quantum gravity which is based on the integration of the tetrad one-forms in the path integral for the Palatini action of General Relativity. In the Euclidian gravity case this…
Mutual information and information entropies in momentum space are proposed as measures of the non-local aspects of information. Singlet and triplet state members of the helium isoelectronic series are employed to examine Coulomb and Fermi…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Understanding the large-scale physics is crucial for the spin foam approach to quantum gravity. We tackle this challenge from a statistical physics perspective using simplified, yet feature-rich models. In particular, this allows us to…
Within the discrete gauge theory which is the basis of spin foam models, the problem of macroscopically faithful coarse graining is studied. Macroscopic data is identified; it contains the holonomy evaluation along a discrete set of loops…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…