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Margarita A. Man'ko

Publications and source records attributed to Margarita A. Man'ko.

31 records · Page 2Linked to original sources
arXiv2014

The maps of matrices and portrait maps of density operators of composite and noncomposite systems

We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. The structure of the maps is inspired by "portrait" map of the probability vectors corresponding to the action on the vectors by stochastic matrices containing either unity or zero matrix elements. We obtain new entropic inequalities for arbitrary qudit states including a single qudit and an discuss entangled single qudit state. We consider in detail the examples of N=3 and 4. Also we point out a possible use of entangled states of systems without subsystems (e.g., a single qudit) as a resource for quantum computations.

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arXiv2014

Wigner function and the probability representation of quantum states

The relation of the Wigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner--Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for direct experimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.

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arXiv2014

Balance equations-based properties of the Rabi Hamiltonian

A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrodinger equation. The knowledge of such properties in the case of Rabi Hamiltonian is exploit to provide arguments to make easier the variational engineering of the ground state of this model.

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arXiv2013

Wigner functions and spin tomograms for qubit states

We establish the relation of the spin tomogram to the Wigner function on a discrete phase space of qubits. We use the quantizers and dequantizers of the spin tomographic star-product scheme for qubits to derive the expression for the kernel connecting Wigner symbols on the discrete phase space with the tomographic symbols.

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arXiv2013

Inequalities for nonnegative numbers and information properties

We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize the degree of quantum correlations in addition to noncontextuality and quantum discord. We use the subadditivity and strong subadditivity conditions for qudit tomographic-probability distributions depending on the unitary-group parameters in order to derive new inequalities for Shannon, Renyi, and Tsallis entropies of spin states.

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arXiv2012

Tomographic entropic inequalities in the probability representation of quantum mechanics

A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the state tomograms which are considered either as a set of the probability distributions of random variables depending on extra parameters or as a single joint probability distribution of these random variables and random parameters with specific properties of the marginals. Examples of optical tomograms of photon states, symplectic tomograms, and unitary spin tomograms of qudits are given. A new universal integral inequality for generic wave function is obtained on the base of tomographic entropic uncertainty relations.

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arXiv2009

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.

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arXiv2006

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.

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arXiv2004

Squeezing Operator and Squeeze Tomography

Some properties of Plebanski squeezing operator and squeezed states created with time-dependent quadratic in position and momentum Hamiltonians are reviewed. New type of tomography of quantum states called squeeze tomography is discussed.

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arXiv1999

Quantum Tomography Approach in Signal Analysis

Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to the fractional Fourier transform is elucidated.

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