Related papers: Can \v{C}encov meet Petz?
In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
Let $G$ be a locally compact group and $P \subset G$ be a closed Ore semigroup containing the identity element. Let $V: P \to B(\clh)$ be a representation such that for every $a \in P$, $V_{a}$ is an isometry and the final projections of…
It is a fundamental, but still elusive question whether the schemes based on quantum mechanics, in particular on quantum entanglement, can be used for classical information processing and machine learning. Even partial answer to this…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…
We show that if $G$ is a second countable locally compact Hausdorff \'etale groupoid carrying a suitable cocycle $c:G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a…
Two areas of mathematics which have received substantial attention in recent years are the theory of optimal transport and the Elliott classification programme for C*-algebras. We combine these two seemingly unrelated disciplines to make…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
We prove Leavitt path algebra versions of the two uniqueness theorems of graph C*-algebras. We use these uniqueness theorems to analyze the ideal structure of Leavitt path algebras and give necessary and sufficient conditions for their…
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes \mathrm{H}_3,$ which arises in the context of quantum gravity. We relate quantum observables…
We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.
We study and solve the problem of classical channel simulation with quantum side information at the receiver. This is a generalization of both the classical reverse Shannon theorem, and the classical-quantum Slepian-Wolf problem. The…
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…
Theorem. There are general position points A, B, C, P on the projective plane. Let A_P be the intersection point of lines AP and BC. Analogously define B_P and C_P. Take any points A_1, B_1, C_1 on AP, BP, CP, respectively. Let W_C be the…
We show that the dimension of the Cuntz semigroup of a C*-algebra is determined by the dimensions of the Cuntz semigroups of its separable sub-C*-algebras. This allows us to remove separability assumptions from previous results on the…
The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present…
A great number of articles widen a known scientific result $P(a)$ (such as: a theorem, an inequality, or a math/physics/chemical etc. proposition or formula) by a simple recurrence procedure and using, in the proof, the proposition $P(a)$…
We investigate deviations from the plane wave model in the interaction of charged particles with strong electromagnetic fields. A general result is that integrability of the dynamics is lost when going from lightlike to timelike or…