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M. A. Man'ko

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

13 recordsLinked to original sources
arXiv2019

Dynamics of a harmonic oscillator coupled with a Glauber amplifier

A system of a quantum harmonic oscillator bi-linearly coupled with a Glauber amplifier is analysed considering a time-dependent Hamiltonian model. The Hilbert space of this system may be exactly subdivided into invariant finite dimensional subspaces. Resorting to the Jordan-Schwinger map, the dynamical problem within each invariant subspace may be traced back to an effective SU(2) Hamiltonian model expressed in terms of spin variables only. This circumstance allows to analytically solve the dynamical problem and thus to study the exact dynamics of the oscillator-amplifier system under specific time-dependent scenarios. Peculiar physical effects are brought to light by comparing the dynamics of such a system with that of two interacting standard oscillators.

quant-ph↗
arXiv2017

New entropic inequalities for qubit and unimodal Gaussian states

The Tsallis relative entropy $S_q (\hatρ,\hatσ)$ measures the distance between two arbitrary density matrices $\hatρ$ and $\hatσ$. In this work the approximation to this quantity when $q=1+δ$ ($δ\ll 1$) is obtained. It is shown that the resulting series is equal to the von Neumann relative entropy when $δ=0$. Analyzing the von Neumann relative entropy for arbitrary $\hatρ$ and a thermal equilibrium state $\hatσ=e^{- β\hat{H}}/{\rm Tr}(e^{- β\hat{H}})$ is possible to define a new inequality relating the energy, the entropy, and the partition function of the system. From this inequality, a parameter that measures the distance between the two states is defined. This distance is calculated for a general qubit system and for an arbitrary unimodal Gaussian state. In the qubit case, the dependence on the purity of the system is studied for $T \geq 0$ and also for $T<0$. In the Gaussian case, the general partition function given a unimodal quadratic Hamiltonian is calculated and the comparison of the thermal light state as a thermal equilibrium state of the parametric amplifier is presented.

quant-ph↗
arXiv2016

Minimal sets of dequantizers and quantizers for finite-dimensional quantum systems

The problem of finding and characterizing minimal sets of dequantizers and quantizers applied in the mapping of operators onto functions is considered, for finite-dimensional quantum systems. The general properties of such sets are determined. An explicit description of all the minimum self-dual sets of dequantizers and quantizers for a qubit system is derived. The connection between some known sets of dequantizers and quantizers and the derived formulae is presented.

quant-ph↗
arXiv2009

Tomographic probability representation for quantum fermion fields

Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are described by fermionic tomographic symbols. The product of the operators acting on the fermion states is mapped onto star-product of the fermionic symbols. The kernel of the star-product is obtained. The antisymmetry of the fermion states is formulated as the specific symmetry property of the tomographic joint probability distribution associated with the states.

quant-ph↗
arXiv2009

Quantum Fourier transform and tomographic Renyi entropic inequalities

Renyi entropy associated with spin tomograms of quantum states is shown to obey to new inequalities containing the dependence on quantum Fourier transform. The limiting inequality for the von Neumann entropy of spin quantum states and a new kind of entropy associated with quantum Fourier transform are obtained. Possible connections with subadditivity and strong subadditivity conditions for tomographic entropies and von Neumann entropies are discussed.

quant-ph↗
arXiv2006

A probabilistic operator symbol framework for quantum information

Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic interpretation, a particular class of operator symbols (tomograms) is proposed as a framework for quantum information problems. Qudit states are identified with maps of the unitary group into the simplex. The image of the unitary group on the simplex provides a geometrical characterization of the nature of the quantum states. Generalized measurements, typical quantum channels, entropies and entropy inequalities are discussed in this setting.

quant-ph↗
arXiv2005

Fresnel tomography: a novel approach to the wave function reconstruction based on Fresnel representation of tomograms

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 probability distribution is elucidated. Multimode generalization of the Fresnel tomography is presented. Examples of applications of the present approach are given.

quant-ph↗
arXiv2002

Tomography of Solitons

We develope the tomographic representation ofwavefunctions which are solutions of the generalizednonlinear Schrodinger equation (NLSE) and show itsconnection with the Weyl--Wigner map.In particular, this theory is applied tothe envelope solitons, where tomograms for envelopebright solitons of a wide family of modified NLSE arepresented and numerically evalueted.

nlin.PS↗
arXiv2002

Modelling Quantum Mechanics by the Quantumlike Description of the Electric Signal Propagation in Transmission Lines

It is shown that the transmission line technology can be suitably used for simulating quantum mechanics. Using manageable and at the same time non-expensive technology, several quantum mechanical problems can be simulated for significant tutorial purposes. The electric signal envelope propagation through the line is governed by a Schrodinger-like equation for a complex function, representing the low-frequency component of the signal, In this preliminary analysis, we consider two classical examples, i.e. the Frank-Condon principle and the Ramsauer effect.

quant-ph↗
arXiv2001

Quantum computation by quantum-like systems

Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and quantum gates to segments of the fiber providing an unitary transformation of the mode structure along a space direction. Simulation of nonlinear quantum effects is also discussed.

quant-ph↗
arXiv2001

Tomograms and other transforms. A unified view

A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the symplectic and affine groups is treated in some detail. Special emphasis is given to the properties of the scale-time and scale-frequency tomograms. Tomograms are interpreted as a tool to sample the signal space by a family of curves or as the matrix element of a projector.

math-ph↗
arXiv1994

Nonclassical Light in Interferometric Measurements

It is shown that the even and odd coherent light and other nonclassical states of light like superposition of coherent states with different phases may replace the squeezed light in interferometric gravitational wave detector to increase its sensitivity. (Contribution to the Second Workshop on Harmonic Oscillator, Cocoyoc, Mexico, March 1994)

hep-th↗