Related papers: Can \v{C}encov meet Petz?
In this paper we study the structure of the $C^*$-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic $C^*$-algebras over this poset. We construct the extensions…
Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
A $C^*$-algebra satisfies the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet if it is equivalent in Kasparov's $KK$-theory to a commutative $C^*$-algebra. This paper is motivated by the problem of establishing the range of…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
Mathematical tools related to coherence theory and classical-quantum equivalence, due to Wigner and Glauber, are essential to modern, practical and empirical understanding of electromagnetics in areas like quantum optics and…
The new emerging quantum physics - quantum computing conceptual bridge, mandates a ``grand unification'' of space-time-matter and quantum information (all quantized), with deep implications for science in general. The major physics…
In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical…
The search for a potential function $S$ allowing to reconstruct a given metric tensor $g$ and a given symmetric covariant tensor $T$ on a manifold $\mathcal{M}$ is formulated as the Hamilton-Jacobi problem associated with a canonically…
We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate…
It is shown that, for a C*-algebra of stable rank one (i.e., in which the invertible elements are dense), two well-known isomorphism invariants, the Cuntz semigroup and the Thomsen semigroup, contain the same information. More precisely,…
Years ago, Itamar Pitowski asked two relevant questions: Why microphysical (quantum) phenomena and classical phenomena differ in the way they do? and, what kind of explanation could qualify as a reasonable one? I argue that both questions…
The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric…
In this correspondence we present a new proof of Holevo's coding theorem for transmitting classical information through quantum channels, and its strong converse. The technique is largely inspired by Wolfowitz's combinatorial approach using…
We introduce a method to define $C^*$-algebras from $C^*$-correspondences. Our construction generalizes Cuntz-Pimsner algebras, crossed products by Hilbert $C^*$-modules, and graph algebras.
We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…
This note gives an introduction to the theories of impedances and wakes in particle accelerators. The standard formulation assumes that the beam is traveling along a straight orbit with constant velocity $\vec{v}=v\vec{e}_z$. On this note,…
Higher rank semigraph algebras are introduced by mixing concepts of ultragraph algebras and higher rank graph algebras. This yields a kind of higher rank generalisation of ultragraph algebras. We prove Cuntz--Krieger uniqueness theorems for…