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

Probability Distributions and Hilbert Spaces: Quantum and Classical Systems

We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular class of linear Hamiltonian systems.Comment: LATEX,13pages,accepted by Physica Scripta (1999

Entropic uncertainty relations for electromagnetic beams

The symplectic tomograms of 2D Hermite--Gauss beams are found and expressed in terms of the Hermite polynomials squared. It is shown that measurements of optical-field intensities may be used to determine the tomograms of electromagnetic-radiation modes. Furthermore, entropic uncertainty relations associated with these tomograms are found and applied to establish the compatibility conditions of the the field profile properties with Hermite--Gauss beam description. Numerical evaluations for some Hermite--Gauss modes illustrating the corresponding entropic uncertainty relations are finally given.Comment: Invited talk at the XV Central European Workshop on Quantum Optics (Belgrade, Serbia, 30 May -- 3 June 2008), to appear in Physica Scripta

Permutation symmetry for the tomographic probability distribution of a system of identical particles

The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution. Explicit calculations are performed in the case of the two-dimensional harmonic oscillator.Comment: 13 pages, latex, no figure

Beyond the Standard "Marginalizations" of Wigner Function

We discuss the problem of finding "marginal" distributions within different tomographic approaches to quantum state measurement, and we establish analytical connections among them.Comment: 12 pages, LaTex, no figures, to appear in Quantum and Semiclass. Op

Distances between quantum states in the tomographic-probability representation

Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are distinguished by comparing corresponding probability-distribution functions. Fidelity as well as other distance measures are expressed in terms of tomograms.Comment: 10 pages, Contribution to the 16th Central European Workshop on Quantum Optics (CEWQO'09), May 23-27, 2009, Turku, Finlan