arXiv subjects

V. I. Manko

Publications and source records attributed to V. I. Manko.

14 recordsLinked to original sources

arXiv2018

New entropic inequalities for qudit(spin j=9/2)

We consider information characteristics of single qudit state (spin j=9/2), such as von Neumann entropy, von Neumann mutual information. We review different mathematical properties of these information characteristics: subadditivity and strong subadditivity conditions, Araki-Lieb inequality. The inequalities are entropic inequalities for composite systems (bipartite, tripartite), but they can be written for noncomposite systems. Using the density matrix, describing the noncomposite qudit system state in explicit matrix form we proved new entropic inequalities for single qudit state (spin j=9/2). In addition, we also consider the von Neumann information of a qudit toy model as a function of a real parameter. The obtained inequalities describe the quantum hidden correlations in the single qudit system.

quant-ph↗

arXiv2017

The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients

We discuss the procedure of different partitions in the finite set of $N$ integer numbers and construct generic formulas for a bijective map of real numbers $s_y$, where $y=1,2,\ldots,N$, $N=\prod \limits_{k=1}^{n} X_k$, and $X_k$ are positive integers, onto the set of numbers $s(y(x_1,x_2,\ldots,x_n))$. We give the functions used to present the bijective map, namely, $y(x_1,x_2,...,x_n)$ and $x_k(y)$ in an explicit form and call them the functions detecting the hidden correlations in the system. The idea to introduce and employ the notion of "hidden gates" for a single qudit is proposed. We obtain the entropic-information inequalities for an arbitrary finite set of real numbers and consider the inequalities for arbitrary Clebsch--Gordan coefficients as an example of the found relations for real numbers.

quant-ph↗

arXiv2017

New information and entropic inequalities for Clebsch-Gordan coefficients

The Clebsch-Gordan coefficients of the group SU(2) are shown to satisfy new inequalities. They are obtained using the properties of Shannon and Tsallis entropies. The inequalities associated with the Wigner 3-j symbols are obtained using the relation of Clebsch-Gordan coefficients with probability distributions interpreted either as distributions for composite systems or distributions for noncomposite systems. The new inequalities were found for Hahn polynomials and hypergeometric functions

quant-ph↗

arXiv2015

Gauge transformation of quantum states in probability representation

The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states under a gauge transformation of electromagnetic field potentials are obtained. Gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions of states of quantum system are introduced, and their evolution equations having the Liouville equation in corresponding representations as the classical limit are found.

quant-ph↗

arXiv2013

Groupoids and the tomographic picture of quantum mechanics

The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit, photon-number (Fock) states and symplectic tomography quantizers and dequantizers will be constructed. Conditions for identifying the convolution product of groupoid functions and the star--product arising from a quantization--dequantization scheme will be given. A tomographic approach to construct quasi--distributions out of suitable immersions of groupoids into Hilbert spaces will be formulated and, finally, intertwining kernels for such generalized symplectic tomograms will be evaluated explicitly.

math-ph↗

arXiv2013

Tomographic Discord and Quantum Correlations for System of Qubits

The difference of quantum mutual information for bipartite system of qubits and minimum taken with respect to local unitary transformation group is introduced as a characteristic of quantum correlations.The two qubits example (and specifically the two qubits X state) is studied in some details.

quant-ph↗

arXiv2013

Bound state of particle in delta-potential in tomographic representation of quantum mechanics

The problem of quantum particle moving in Dirac delta potential with instant changing well depth is studied by using formalism of tomographic representation of quantum mechanics.The bound state tomogram is given in terms of error function.The ionisation probability due to instant change of the potential parameter is calculated in terms of integral containing the state tomograms.The probability of ionisation is also expressed in terms of the Wigner function.

quant-ph↗

arXiv2013

Wave function of classical particle in linear potential

The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying von Newmann-like equation in the form of product of wave functions. The relation to quantum mechanics is discussed.

quant-ph↗

arXiv2012

A pedagogical presentation of a $C^\star$-algebraic approach to quantum tomography

It is now well established that quantum tomography provides an alternative picture of quantum mechanics. It is common to introduce tomographic concepts starting with the Schrodinger-Dirac picture of quantum mechanics on Hilbert spaces. In this picture states are a primary concept and observables are derived from them. On the other hand, the Heisenberg picture,which has evolved in the $C^\star-$algebraic approach to quantum mechanics, starts with the algebra of observables and introduce states as a derived concept. The equivalence between these two pictures amounts essentially, to the Gelfand-Naimark-Segal construction. In this construction, the abstract $% C^\star-$algebra is realized as an algebra of operators acting on a constructed Hilbert space. The representation one defines may be reducible or irreducible, but in either case it allows to identify an unitary group associated with the $C^\star-$algebra by means of its invertible elements. In this picture both states and observables are appropriate functions on the group, it follows that also quantum tomograms are strictly related with appropriate functions (positive-type)on the group. In this paper we present, by means of very simple examples, the tomographic description emerging from the set of ideas connected with the $C^\star-$algebra picture of quantum mechanics. In particular, the tomographic probability distributions are introduced for finite and compact groups and an autonomous criterion to recognize a given probability distribution as a tomogram of quantum state is formulated.

quant-ph↗

arXiv2005

Partial positive scaling transform: a separability criterion

The problem of constructing a necessary and sufficient condition for establishing the separability of continuous variable systems is revisited. Simon [R. Simon, Phys. Rev. Lett. 84, 2726 (2000)] pointed out that such a criterion may be constructed by drawing a parallel between the Peres' partial transpose criterion for finite dimensional systems and partial time reversal transformation for continuous variable systems. We generalize the partial time reversal transformation to a partial scaling transformation and re-examine the problem using a tomographic description of the continuous variable quantum system. The limits of applicability of the entanglement criteria obtained from partial scaling and partial time reversal are explored.

quant-ph↗

arXiv2004

Radon transform of Wheeler-De Witt equation and tomography of quantum states of the universe

The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability distribution with the Wigner function of the universe and with the star-product (deformation) quantization procedure is established. Using the Radon transform the Wheeler-De Witt generic equation for the probability function is written in tomographic form. Some examples of the Wheeler-DeWitt equation in the minisuperspace are elaborated explicitly for a homogeneous isotropic cosmological models. Some interpretational aspects of the probability description of the quantum state are discussed.

gr-qc↗

arXiv2001

Geometrical Aspects of Lie Groups Representations and Their Optical Applications

In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in quantum-optics problems.

quant-ph↗

arXiv1997

Particles and Nuclei as Quantum Slings

Rotation of such objects as an atomic nucleus or a chromodynamical string can result in specific effects in scattering processes and multiparticle production. Secondary fragments of the rotating nucleus or of the decaying string can move like stones thrown from a sling. That would be detected as the azimuthal asymmetry of particle distributions in individual events. Non-classical states of the created particles like the Schr"\{o}dinger cats are produced. Some classical and quantum-mechanical estimates of possible effects are given. Experimental facts which can be used for their verification are discussed.

hep-ph↗

arXiv1996

Correlated states and Schrödinger cats

The Schrödinger cat male and female states are discussed. The Wigner and Q--functions of generalized correlated light are given. Linear transformator of photon statistics is reviewed.

quant-ph↗