Related papers: Gamma Spaces and Information
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
Many important results in modern quantum information theory have been obtained for an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a…
We model equivariant infinite loop spaces indexed on incomplete universes via suitable equivariant analogs of $\Gamma$-spaces. The choice of universe dictates a transfer system which in turn dictates the Segal condition on equivariant…
The paper examines machines of the type of the $\Gamma$-spaces of Segal which describe homotopy structures on topological spaces. The main result of the paper shows that for any such machine one can find an algebraic theory characterizing…
The interplay between two basic quantities -- quantum communication and information -- is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement.…
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
We construct a completed version C(Gamma) of the configuration space of a linkage Gamma in R^3 which takes into account the ways one link can touch another. We also describe a simplified version of C(Gamma) which is a blow-up of the space…
It is shown on a simple classical model of a quantum particle at rest that information contained into the quantum state (quantum information) can be obtained by integrating the corresponding probability distribution on phase space, i.e. by…
This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced…
We relate the notions of spectral gap for unitary representations and subfactors with definability of certain important sets in the corresponding structures. We give several applications of this relationship.
The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process…
In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The…
Modeling electromagnetic cascades during gamma-ray transport is important in many applications within astrophysics. This document introduces $\gamma$-Cascade, a publicly available Mathematica package which allows users to calculate observed…
Some formal aspects of the Semantic Spacetime graph model are presented, with reference to its use for directed knowledge representations and process modelling. A finite $\gamma(3,4)$ representation is defined to form a closed set of…
We establish a quantitative connection between the amount of lost classical information about a quantum state and the concomitant loss of entanglement. Using methods that have been developed for the optimal purification of mixed states we…
The spectral gap occupies a role of central importance in many open problems in physics. We present an approach for evaluating the spectral gap of a Hamiltonian from a simple ratio of two expectation values, both of which are evaluated…
Quantum information can provide a lens for characterizing the operational implications of spacetime physics. A well-known result in this area is that quantum entanglement is degraded in the vicinity of a black hole. This result treats the…
The Gamma-class is a characteristic class for complex manifolds with transcendental coefficients. It defines an integral structure of quantum cohomology, or more precisely, an integral lattice in the space of flat sections of the quantum…
These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary…
In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic…