Related papers: Can \v{C}encov meet Petz?
Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
We calculate the Cuntz semigroup of the tensor product A with A. We restrict our attention to C*-algebras A which are unital, simple, nuclear, stably finite, have stable rank one, absorbs the Jiang-Su algebra tensorially and satisfy the…
We prove new inner bounds for several multiterminal channels with classical inputs and quantum outputs. Our inner bounds are all proved in the one-shot setting, and are natural analogues of the best classical inner bounds for the respective…
Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…
The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we…
Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's…
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing…
Most coding theorems in quantum Shannon theory can be proven using the decoupling technique: to send data through a channel, one guarantees that the environment gets no information about it; Uhlmann's theorem then ensures that the receiver…
We develop the theory of CW(A)-complexes, which generalizes the classical theory of CW-complexes, keeping the geometric intuition of J.H.C. Whitehead's original theory. We obtain this way generalizations of classical results, such as…
We introduce a bivariant version of the Cuntz semigroup as equivalence classes of order zero maps generalizing the ordinary Cuntz semigroup. The theory has many properties formally analogous to KK-theory including a composition product. We…
Recent advances in our understanding of foundations of quantum mechanics have shown that information can be made objective through quantum states. Such objectification processes, predicted e.g. in a variety of quantum open systems, must…
We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as…
String diagrams turn algebraic equations into topological moves that have recurring shapes, involving the sliding of one diagram past another. We individuate, at the root of this fact, the dual nature of polygraphs as presentations of…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…
To formulate a universal framework of information theory is beneficial. This study proves that the sextuple model of the objective information theory (OIT) is a sufficient and necessary condition for discussing information with four basic…
This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum…
Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic…
In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism within the framework of information geometry. In this paper, we formulate a correspondence…