相关论文: Tomograms and other transforms. A unified view
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
The tomographic map of quantum state of a system with several degrees of freedom which depends on one random variable, analogous to center of mass considered in rotated and scaled reference frame in the phase space, is constructed. Time…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
Tomograms introduced for the description of quantum states in terms of probability distributions are shown to be related to a standard star-product quantization with appropriate kernels. Examples of symplectic tomograms and spin tomograms…
We introduce several possible generalizations of tomography for quadratic surfaces. We analyze different types of elliptic, hyperbolic and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
A sample of some relevant developments that have taken place during the last twenty years in classical and quantum tomography are displayed. We will present a general conceptual framework that provides a simple unifying mathematical picture…
We present here a set of lecture notes on tomography. The Radon transform and some of its generalizations are considered and their inversion formulae are proved. We will also look from a group-theoretc point of view at the more general…
New type of tomographic probability distribution, which contains complete information on the density matrix (wave function) related to the Fresnel transform of the complex wave function, is introduced. Relation to symplectic tomographic…
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
The classic imaging geometry for computed tomography is for collection of un-truncated projections and reconstruction of a global image, with the Fourier transform as the theoretical foundation that is intrinsically non-local. Recently,…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
A review of the photon-number tomography and symplectic tomography as examples of star-product quantization is presented. The classical statistical mechanics is considered within the framework of the tomographic representation.
Amongst the multitude of state reconstruction techniques, the so-called "quantum tomography" seems to be the most fruitful. In this letter, I will start by developing the mathematical apparatus of quantum tomography and, later, I will…
Diffraction tomography is a widely used inverse scattering technique for quantitative imaging of weakly scattering media. In its conventional formulation, diffraction tomography assumes monochromatic plane wave illumination. This…