Browsing by Author "Klyachko, A. A."
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Item Open Access Angular momentum of photons emitted by atoms(Institute of Physics Publishing Ltd., 2004) Can, M. A.; Çakır, Ö.; Horzela, A.; Kapuscik, E.; Klyachko, A. A.; Shumovsky, A. S.It is shown that the spin and orbital angular momentum of electric dipole photons have the same operator structure and may differ from each other only in the spatial dependence in the very vicinity of the atom. It is shown that the photon twins created by a dipole forbidden transition can manifest the maximum entanglement with respect to the angular momentum. It is shown that the states of photons with a projection of angular momentum m = 0 are less stable than those with m = ±1.Item Open Access Correlations between the ranks of submatrices and weights of random codes(2009) Klyachko, A. A.; Özen, I.The results of our study are twofold. From the random matrix theory point of view we obtain results on the rank distribution of column submatrices. We give the moments and the covariances between the ranks (q- rank) of such submatrices. We conjecture the counterparts of these results for arbitrary submatrices. The case of higher correlations gets drastically complicated even in the case of three submatrices. We give a formula for the correlation of ranks of three submatrices and a conjecture for its closed form. From the code theoretical point of view our study yields the covariances of the coefficients of the weight enumerator of a random code. Particularly interesting is that the coefficients of the weight enumerator of a code with random parity check matrix are uncorrelated. We give a conjecture for the triple correlations between the coefficients of the weight enumerator of a random code. © 2009 Elsevier Inc. All rights reserved.Item Open Access Entanglement and the SU(2) phase states in atomic systems(American Physical Society, 2002) Can, M. A.; Klyachko, A. A.; Shumovsky, A. S.For the system of two identical two-level atoms interacting with a single photon, it is shown that the maximum entangled atomic states are represented by the SU(2) phase states of spin 1/2. Furthermore, it is shown that the SU(2) phase states of the half-integer spin j for a certain class of maximum entangled atomic states in the system of 2n atoms interacting with n photons. In particular, the violation of classical realism is shown.Item Open Access Entanglement of a single spin-1 object: An example of ubiquitous entanglement(Springer New York LLC, 2007) Binicioǧlu, S.; Can, M. A.; Klyachko, A. A.; Shumovsky, A. S.Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. [A.A. Klyachko and A.S. Shumovsky, J. Phys: Conf. Series 36, 87 (2006), E-print quant-ph/0512213]. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered.Item Open Access Entanglement of qutrits(Institute of Physics Publishing Ltd., 2007) Klyachko, A. A.; Öztop, B.; Shumovsky, A. S.For two types of qutrits specified by the dynamical symmetry SU(3) and SU(2), we consider the difference in entanglement caused by the lack of quantum observables in the latter case. In particular, we show that the SU(2) qutrits can have specific separable entanglement caused by quantum correlations of intrinsic degrees of freedom in a single party without interparty correlations. © Nauka/Interperiodica 2007.Item Open Access Entanglement, local measurements and symmetry(Institute of Physics Publishing, 2003) Klyachko, A. A.; Shumovsky, A. S.AbstractAdefinition of entanglement in terms of local measurements is discussed.Namely, the maximum entanglement corresponds to the states that cause thehighest level of quantum fluctuations in all local measurements determinedby the dynamic symmetry group of the system. A number of examplesillustrating this definition is consideredItem Open Access General approach to quantum entanglement(Institute of Physics Publishing Ltd., 2007) Klyachko, A. A.; Shumovsky, A. S.We examine quantum entanglement as a physical phenomenon independent of specific problems of quantum information technologies. Within the dynamic symmetry approach, we briefly discuss the role of quantum fluctuations in formation of entangled states, including single-particle entanglement, relativity of entanglement with respect to the choice of basic observables, and stabilization of robust entanglement.Item Open Access Generic entangled states as the su(2) phase states(World Scientific Publishing, 2005) Binicioǧlu, S.; Çakir, Ö.; Klyachko, A. A.; Shumovsky, A. S.We discuss an algebraic way to construct generic entangled states of qunits based on the polar decomposition of the su(2) algebra. In particular, we show that these states can be defined as eigenstates of certain Hermitian operators.Item Restricted Maximum entanglement(Institute of Physics Publishing, 2003-08) Klyachko, A. A.; Shumovsky, A. S.We discuss a novel variational principle in quantummechanics defining maximum entangled states in terms of quantum fluctuations of observables specifying these stales.Item Open Access Maximum entanglement and its proper measure(Institute of Physics, 2004) Klyachko, A. A.; Shumovsky, A. S.We discuss a definition of maximally entangled states in terms of maximum uncertainty of corresponding measurements. We describe a method of construction of bases of maximally entangled states. The entangled states that can be obtained from the maximally entangled states by means of SLOCC (stochastic local operations assisted by classical communications) we consider as semistable vectors. We discuss a measure of entanglement expressed in terms of a geometric invariant.Item Open Access Operational measure of entanglement for pure states of bipartite systems(Akademiai Kiado Rt., 2006-03) Klyachko, A. A.; Öztop, B.; Shumovsky, A. S.We show that the complete information about the amount of entanglement carried by a bipartite pure state of any dimension (qubits, qutrits, etc), is determined by a local quantity that can be measured for either party of the system. This quantity is expressed in terms of averages of certain basic observables. In particular case of two entangled photon beams, this corresponds to the measurement of three Stokes parameters for either beam.Item Open Access Persistent perfect entanglement in atomic systems(Institute of Physics Publishing, 2004) Çakir, Ö.; Can, M. A.; Klyachko, A. A.; Shumovsky, A. S.It is show that the system of an even number of three-level atoms in the A configuration in a cavity can evolve into a persistent maximum entangled state. The time of formation or such an entangled state is estimated.Item Open Access The problem of localizing photons(Institute of Physics Publishing, 2001-01) Shumovsky, A. S.; Klyachko, A. A.It is shown that the boundary conditions, specifying the plane waves of photons, are incapable of description of the photon localization at detection and emission. It is also shown that deflection from the plane waves causes an important change (deterioration) of the quantum limit of precision of different photonic measurements.Item Open Access Quantification of entanglement via uncertainties(American Physical Society, 2007) Klyachko, A. A.; Öztop, B.; Shumovsky, A. S.We show that entanglement of pure multiparty states can be quantified by means of quantum uncertainties of certain basic observables through the use of a measure that was initially proposed by Klyachko.Item Open Access Simple test for hidden variables in spin-1 systems(2008) Klyachko, A. A.; Can, M. A.; Binicioǧlu, S.; Shumovsky, A. S.We resolve an old problem about the existence of hidden parameters in a three-dimensional quantum system by constructing an appropriate Bell's type inequality. This reveals the nonclassical nature of most spin-1 states. We shortly discuss some physical implications and an underlying cause of this nonclassical behavior, as well as a perspective of its experimental verification. © 2008 The American Physical Society.Item Open Access Squeezed and entangled states of a single spin(Institute of Physics, University of Lodz, 2007-03-01) Öztop, B.; Klyachko, A. A.; Shumovsky, A. S.We show correspondence between the notions of spin squeezing and spin entanglement. We propose a new measure of spin squeezing. We consider a number of physical examples.Item Open Access Stable bundles, representation theory and Hermitian operators(Birkhaeuser Science, 1998) Klyachko, A. A.We give an interpretation and a solution of the classical problem of the spectrum of the sum of Hermitian matrices in terms of stable bundles on the projective plane. ©Birkhäuser Verlag, Basel, 1998.Item Open Access Stationary entanglement of atoms induced by classical field(American Institute of Physics, 2005) Çakir, Ö.; Klyachko, A. A.; Shumovsky, A. S.We propose a scheme of stabilization of high-level entanglement through the use of classical driving field in atomic system with dipole-dipole interaction and losses caused by spontaneous radiation processes. © 2005 American Institute of Physics.Item Open Access Steady-state bipartite entanglement supported by a squeezed environment(Institute of Physics Publishing, 2005-05) Can, M. A.; Çakir, Ö.; Günhan, A. C.; Klyachko, A. A.; Pak, N. K.; Shumovsky, A. S.We examine the entanglement of two atoms induced by an external quantum system. Both two-level atoms are coupled to a third two-level system by dipole interaction, and the third system is under the influence of a certain environment. We examine different types of environments and show that the steady-state bipartite entanglement can be achieved. We show that a strongly fluctuating environment is more preferable because the transmission of quantum fluctuations to the atomic system creates and supports steady-state entanglement with a higher amount of concurrence than a nonfluctuating environment or an environment with strong classical fluctuations.Item Open Access Steady-state entanglement of two atoms created by classical driving field(American Physical Society, 2005) Çakir, Ö.; Klyachko, A. A.; Shumovsky, A. S.The stabilization of entanglement caused by action of a classical driving field in the system of two-level atoms with the dipole interaction accompanied by spontaneous emission is discussed. An exact solution shows that the maximum amount of concurrence that can be achieved in the Lamb-Dicke limit is 0.43. Dependence of entanglement on interatomic distance and the classical driving field, beyond the Lamb-Dicke limit, is examined numerically. © 2005 The American Physical Society.