On the tomographic description of classical fields

After a general description of the tomographic picture for classical systems, a tomographic description of free classical scalar fields is proposed both in a finite cavity and the continuum. The tomographic description is constructed in analogy with the classical tomographic picture of an ensemble of harmonic oscillators. The tomograms of a number of relevant states such as the canonical distribution, the classical counterpart of quantum coherent states and a new family of so called Gauss--Laguerre states, are discussed. Finally the Liouville equation for field states is described in the tomographic picture offering an alternative description of the dynamics of the system that can be extended naturally to other fields

New uncertainty relations for tomographic entropy: Application to squeezed states and solitons

Using the tomographic probability distribution (symplectic tomogram) describing the quantum state (instead of the wave function or density matrix) and properties of recently introduced tomographic entropy associated with the probability distribution, the new uncertainty relation for the tomographic entropy is obtained. Examples of the entropic uncertainty relation for squeezed states and solitons of the Bose--Einstein condensate are considered.Comment: 18 pages, 2 figures, to be published in European Physical Journal

Bell's inequalities in the tomographic representation

The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be the most natural one to compare the predictions of classical and quantum theory. Examples of inequalities for two qubits an two qutrits are considered in the tomographic probability representation of spin states.Comment: 11 pages, comments and references adde

Quantum tomography and nonlocality

We present a tomographic approach to the study of quantum nonlocality in multipartite systems. Bell inequalities for tomograms belonging to a generic tomographic scheme are derived by exploiting tools from convex geometry. Then, possible violations of these inequalities are discussed in specific tomographic realizations providing some explicit examples.Comment: 23 pages, 2 figures, contribution to the special issue of Physica Scripta celebrating 150 years of Margarita and Vladimir I. Man'k

Tomographic Image Reconstruction of Fan-Beam Projections with Equidistant Detectors using Partially Connected Neural Networks

We present a neural network approach for tomographic imaging problem using interpolation methods and fan-beam projections. This approach uses a partially connected neural network especially assembled for solving tomographic\ud reconstruction with no need of training. We extended the calculations to perform reconstruction with interpolation and to allow tomography of fan-beam geometry. The main goal is to aggregate speed while maintaining or improving the quality of the tomographic reconstruction process

Radon transform on the cylinder and tomography of a particle on the circle

The tomographic probability distribution on the phase space (cylinder) related to a circle or an interval is introduced. The explicit relations of the tomographic probability densities and the probability densities on the phase space for the particle motion on a torus are obtained and the relation of the suggested map to the Radon transform on the plane is elucidated. The generalization to the case of a multidimensional torus is elaborated and the geometrical meaning of the tomographic probability densities as marginal distributions on the helix discussed.Comment: 9 pages, 3 figure

Quantum tomography for Dirac spinors

We present a tomographic scheme, based on spacetime symmetries, for the reconstruction of the internal degrees of freedom of a Dirac spinor. We discuss the circumstances under which the tomographic group can be taken as SU(2), and how this crucially depends on the choice of the gamma matrix representation. A tomographic reconstruction process based on discrete rotations is considered, as well as a continuous alternative.Comment: 9 pages, LaTeX; v2: minor changes, references added. A slightly revised version has been accepted for publication in Phys. Lett.