相关论文: Tomograms and other transforms. A unified view

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the…

We highlight the important role of the Fourier transform in deriving inversion formulas for the integral transforms of tomographic imaging. We demonstrate this principle by deriving inversion formulas for the divergent beam transform and…

Quantum tomography can reconstruct fine phase-space structures that are not necessarily resolved by measurement itself. We show that the effective resolution of tomography is determined by a sampling operator linked to the Gram matrix of…

It is shown that the set of optical quantum tomograms can be provided with the topology of Frechet space. In such a case the conjugate space will consist of symbols of quantum observables including all polynomials of the position and…

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

Quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. Here we propose and theoretically investigate a new quantum interferometric scheme based on three-dimensional waveguide devices.…

The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…

This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density…

We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We…

Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…

In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…

The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…

In the shape analysis approach to computer vision problems, one treats shapes as points in an infinite-dimensional Riemannian manifold, thereby facilitating algorithms for statistical calculations such as geodesic distance between shapes…

This paper introduces two-dimensional diagrams that are slight generalizations of moment map images for toric four-manifolds and catalogs techniques for reading topological and symplectic properties of a symplectic four-manifold from these…

In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a…

A graph with a semiregular group of automorphisms can be thought of as the derived cover arising from a voltage graph. Since its inception, the theory of voltage graphs and their derived covers has been a powerful tool used in the study of…

The generic singularities and bifurcations are classified for one-parameter families of curves with frames in a space form, the Euclidean space, the elliptic space or the hyperbolic space via projective geometry. Two kinds of frames are…

Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…

Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for computing integrals and sampling from distributions on algebraic…

The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…