Related papers: Geometry of Information: classical and quantum asp…
The aim of the present paper is twofold. First, to give the main ideas behind quantum computingand quantum information, a field based on quantum-mechanical phenomena. Therefore, a shortreview is devoted to (i) quantum bits or qubits (and…
Quantum information science is presented in a fashion that may be useful to a device or materials engineer. Spintronic implementations are emphasized.
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
We describe a number of geometric contexts where categorification appears naturally: coherent sheaves, constructible sheaves and sheaves of modules over quantizations. In each case, we discuss how "index formulas" allow us to easily perform…
In this note we highlight some connections of UMAP to the basic principles of Information Geometry. Originally, UMAP was derived from Category Theory observations. However, we posit that it also has a natural geometric interpretation.
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
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…
Phenomenological and theoretical aspects of fragmentation for elementary particles (resp. nuclei) are discussed. It is shown that some concepts of classical fragmentation remain relevant in a microscopic framework, exhibiting non-trivial…
This work is a discussion on the concept of information. We define here information as an abstraction that is able to be copied. We consider the connection between the process of copying information in quantum systems and the emergence of…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
A preliminary model of meaningful quanta of information arising from the quantum vacuum, and giving rise to the elementary quantum fields, is presented. We attempt to establish an equivalence of information and physical action, with the…
We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as…
The free Fock space with corresponding - information creation and anihilation operators - supplies a kind of extended language in which equations for n-point information (n-pi) of classical and quantum physics are described. In this…
In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories.…
A formal model of the structure of information is presented in five axioms which define identity, containment, and joins of infons. Joins are shown to be commutative, associative, provide inverses of infons, and, potentially, have many…
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
We present a theory for modeling the structure of information and a language (Quanta) expressing the theory. Unlike Shannon's information theory, which focuses on the amount of information in an information system, we focus on the structure…
Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from…