arXiv subjects

E. B. Fel'dman

Publications and source records attributed to E. B. Fel'dman.

At least 37 records · Page 2Linked to original sources

arXiv2018

Transfer of scaled multiple quantum coherence matrices

Multiple quantum (MQ) NMR coherence spectra, which can be obtained experimentally in MQ NMR, can be transferred from the sender to the remote receiver without mixing the MQ-coherences of different orders and distortions. The only effect of such transfer is scaling of the certain blocks of sender's density matrix (matrices of MQ-coherences of different order). Such a block-scaled transfer is an alternative to the perfect state transfer. In particular, equal scaling of higher order MQ-coherences matrices is possible. Moreover, there are states which can be transferred to the receiver preserving their zero-order coherence matrix. The examples of block-scaled transfer in spin-1/2 communication lines of 6 and 42 nodes with two-qubit sender and receiver are presented.

quant-ph↗

arXiv2018

Theoretical investigations of quantum correlations in NMR multiple-pulse spin-locking experiments

Quantum correlations are investigated theoretically in a two-spin system with the dipole-dipole interactions in the NMR multiple-pulse spin-locking experiments. We consider two schemes of the multiple-pulse spin-locking. The first scheme consists of $π/2$-pulses only and the delays between the pulses can differ. The second scheme contains $φ$-pulses ($0<φ<π$) and has equal delays between them. We calculate entanglement for both schemes for an initial separable state. We show that entanglement is absent for the first scheme at equal delays between $π/2$-pulses at arbitraty temperatures. Entanglement emerges after several periods of the pulse sequence in the second scheme at $φ=π/4$ at milliKelvin temperatures. The necessary number of the periods increases with increasing temperature. We demonstrate the dependence of entanglement on the number of the periods of the multiple-pulse sequence. Quantum discord is obtained for the first scheme of the multiple-pulse spin-locking experiment at different temperatures.

quant-ph↗

arXiv2017

Coherence evolution and transfer supplemented by state-restoring

The evolution of quantum coherences comes with a set of conservation laws provided that the Hamiltonian governing this evolution conserves the spin-excitation number. At that, coherences do not intertwist during the evolution. Using the transmission line and the receiver in the initial ground state we can transfer the coherences to the receiver without interaction between them, { although the matrix elements contributing to each particular coherence intertwist in the receiver's state. } Therefore we propose a tool based on the unitary transformation at the receiver side to { untwist these elements and thus} restore (at least partially) the structure of the sender's initial density matrix. A communication line with two-qubit sender and receiver is considered as an example of implementation of this technique.

quant-ph↗

arXiv2017

Dynamical storage of quantum states

We consider a dynamical method of storage of quantum states based on the spin-1/2 systems with the dipole-dipole interactions in a strong external magnetic field { supplemented with the special time-reversion procedure}. The stored information can be extracted at certain time instants.

quant-ph↗

arXiv2017

Experimental and theoretical investigations of quantum state transfer and decoherence processes in quasi-one-dimensional systems in multiple-quantum NMR experiments

Multiple quantum (MQ) NMR methods \cite{Baum} are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian \cite{Baum} describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of \BPChem{\^{19}F} nuclei in calcium fluorapatite \BPChem{Ca\_5(PO\_4)\_3F}. Relaxation of the MQ NMR coherences is considered as the simplest model of decoherence processes. A theory of the dipolar relaxation of the MQ NMR coherences in one-dimensional systems is developed. A good agreement of the theoretical predictions and the experimental data is obtained.

quant-ph↗

arXiv2016

Temperature-dependent remote control of polarization and coherence intensity with pure sender's initial state

We study the remote creation of the polarization and intensity of the first-order coherence (or coherence intensity) in long spin-1/2 chains with one qubit sender and receiver. Therewith we use a physically motivated initial condition with the pure state of the sender and the thermodynamical equilibrium state of the other nodes. The main part of the creatable region is a one-to-one map of the initial-state (control) parameters, except the small subregion twice covered by the control parameters, which appears owing to the chosen initial state. The polarization and coherence intensity behave differently in the state creation process. In particular, the coherence intensity can not reach any significant value unless the polarization is large in long chains (unlike the short ones), but the opposite is not true. The coherence intensity vanishes with an increase in the chain length, while the polarization (by absolute value) is not sensitive to this parameter. We represent several characteristics of the creatable polarization and coherence intensity and describe their relation to the parameters of the initial state. The link to the eigenvalue-eigenvector parametrization of the receiver's state-space is given.

quant-ph↗

arXiv2015

Contributions of different parts of spin-spin interactions to quantum correlations in a spin ring model in an external magnetic field

We study quantum correlations in a bipartite heteronuclear $(N-1)\times1$ system in an external magnetic field. The system consists of a spin ring with an arbitrary number $N-1$ of spins on the ring and one spin in its center. The spins on the ring are connected by secular dipole-dipole interactions and interact with the central spin through the Heisenberg $zz$-interaction. We show that the quantum discord, describing quantum correlations between the ring and the central spin, can be obtained analytically for this model in the high temperature approximation. The model allows us to find contributions of different parts of the spin-spin interactions to quantum correlations. We also investigate the evolution of quantum and classical correlations at different numbers of spins.

quant-ph↗

arXiv2015

Systems with stationary distribution of quantum correlations: open spin-1/2 chains with XY interaction

Although quantum correlations in a quantum system are characterized by the evolving quantities (which are entanglement and discord usually), we reveal such basis (i.e. the set of virtual particles) for the representation of the density matrix that the entanglement and/or discord between any two virtual particles in such representation are stationary. In particular, dealing with the nearest neighbor approximation, this system of virtual particles is represented by the $β$-fermions of the Jordan-Wigner transformation. Such systems are important in quantum information devices because the evolution of quantum entanglement/discord leads to the problems of realization of quantum operations. The advantage of stationary entanglement/discord is that they are completely defined by the initial density matrix and by the Hamiltonian governing the quantum dynamics in the system under consideration. Moreover, using the special initial condition together with the special system's geometry, we construct large cluster of virtual particles with the same pairwise entanglement/discord. In other words, the measure of quantum correlations is stationary in this system and correlations are uniformly "distributed" among all virtual particles. As examples, we use both homogeneous and non-homogeneous spin-1/2 open chains with XY-interaction although other types of interactions might be also of interest.

quant-ph↗

arXiv2014

Robust stationary distributed discord in Jordan-Wigner fermion system under perturbations of initial state

We investigate the Jordan-Wigner fermion clusters with the stationary distributed pairwise quantum discord. Such clusters appear after the Jordan-Wigner transformation of a spin chain governed by the nearest-neighbor XY-Hamiltonian with the particular initial state having one polarized node. We show that the quantum discord stationarity in such systems is not destroyed by the "parasitic" polarization of at least two types. First type appears because the initial state with a single polarized node is hardly realizable experimentally, so that the low polarization of neighboring nodes must be taken into account. Second, the additional noise-polarization of all nodes is unavoidable. Although the stationarity may not be destroyed by perturbations of the above two types, the parasitic polarizations deform the distribution of the pairwise discord and may destroy the clusters of correlated fermions with equal pairwise discords. Such deformations are studied in this paper.

quant-ph↗

arXiv2013

Calculation of the quantum discord in many-qubit systems

For the first time, we compute the quantum discord in bipartite systems containing up to nine qubits. An analytical expression is obtained for the discord in a bipartite system with three qubits. The dependence of the discord on the temperature and the structural parameter of the model is studied.

quant-ph↗

arXiv2012

Quantum correlations in a system of nuclear s=1/2 spins in a strong magnetic field

Entanglement and quantum discord for a pair of nuclear spins $s=1/2$ in a nanopore filled with a gas of spin-carrying molecules (atoms) are studied. The correlation functions describing dynamics of dipolar coupled spins in a nanopore are found. The dependence of spin-pair entanglement on the temperature and the number of spins is obtained from the reduced density matrix, which is centrosymmetric (CS). An analytic expression for the concurrence is obtained for an arbitrary CS density matrix. It is shown that the quantum discord as a measure of quantum correlations attains a significant value at low temperatures. It is shown also that the discord in the considered model has "flickering" character and disappears periodically in the course of the time evolution of the system. The geometric discord is studied for arbitrary $4\times 4$ CS density matrices.

quant-ph↗

arXiv2012

Quantum correlations in different density matrix representations of spin-1/2 open chain

We consider quantum correlations in a spin-1/2 open chain of $N$ nodes with the XY Hamiltonian using different bases for the density matrix representation and the initial state with a single polarized node. These bases of our choice are following: (i) the basis of eigenvectors of the fermion operators; this basis appears naturally through the Jordan-Wigner transformation (this representation of the density matrix is referred to as the $β$-representation), (ii) its Fourier representation ($c$-representation of the density matrix) and (iii) the basis of eigenvectors of the operators $I_{jz}$ (the $z$-projection of the $j$th spin, $j=1,...,N$). Although for the short chains (a few nodes) the qualitative behavior of the entanglement and the discord are very similar (the difference is quantitative), this is not valid for longer chains ($N\gtrsim 10$). In this case, there are qualitative and quantitative distinctions between the entanglement and the discord in all three cases. We underline three most important features: (i) the quantum discord is static in the $β$-representation, where the entanglement is identical to zero; (ii) in the $c$-representation, the concurrence may be non-zero only between the nearest neighbors (with a single exception), while the discord is nonzero between any two nodes; (iii) there is so-called "echo" in the evolution of the discord, which is not observed in the evolution of the concurrence. Using different bases, we may choose the preferable behavior of quantum correlations which allows a given quantum system to be more flexible in applications.

quant-ph↗

arXiv2011

The effect of spin-lattice relaxation on multiple-quantum NMR coherences in solids

A phenomenological theory of spin-lattice relaxation of multiple-quantum coherences in systems of two dipolar coupled spins at low temperatures is developed. Intensities of multiple-quantum NMR coherences depending on the spin-lattice relaxation time are obtained. It is shown that the theory is also applicable to finite spin chains when the approximation of nearest neighbour interaction is used. An application of this theory to an estimation of the influence of decoherence processes on quantum entanglement and its fluctuations is briefly discussed.

quant-ph↗

arXiv2011

Multiple quantum NMR dynamics in a gas of spin-carrying molecules in fluctuating nanopores

The effect of Gaussian fluctuations of nanopores filled with a gas of spin-carrying molecules ($s=1/2$) on the multiple quantum (MQ) NMR dynamics is investigated at different variances and correlation times of the fluctuations. We show that the fluctuations smooth out the evolution of MQ NMR coherence intensities which rapidly oscillate as functions of time in the absence of fluctuations. The growth and decay of the MQ coherence clusters in the fluctuating nanopore are also investigated.

quant-ph↗

arXiv2011

Asymmetry of bipartite quantum discord

It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmour frequencies at both T=0 (the ground state) and $T>0$ has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with the decrease in temperature.

quant-ph↗

arXiv2011

The multiple quantum NMR dynamics in systems of equivalent spins with the dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an investigation of the MQ NMR dynamics in the systems consisting of hundreds of spins from "the first principles". We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for the systems of $200 - 600$ spins. It is shown that these profiles may be well approximated by the exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, namely the dipolar ordered state and the thermal equilibrium state in the strong external magnetic field.

physics.chem-ph↗

arXiv2010

Numerical analysis of relaxation times of multiple quantum coherences in the system with a large number of spins

We study the decay of multiple quantum (MQ) NMR coherences in systems with the large number of equivalent spins. As being created on the preparation period of MQ NMR experiment, they decay due to the dipole-dipole interactions (DDI) on the evolution period of this experiment. It is shown that the relaxation time decreases with the increase in MQ coherence order {(according to the known results)} and in the number of spins. We also consider the modified preparation period of MQ NMR experiment (G.A.Alvarez, D.Suter, PRL {\bf 104}, 230403 (2010)) concatenating the short evolution periods under the secular DDI Hamiltonian (the perturbation) with the evolution period under the non-secular averaged two-spin/two-quantum Hamiltonian. The influence of the perturbation on the decoherence rate is investigated for the systems consisting of 200-600 equivalent spins.

quant-ph↗

arXiv2010

High probability state transfer in spin-1/2 chains: Analytical and numerical approaches

This article is devoted to the development of analytical and numerical approaches to the problem of the end-to-end quantum state transfer along the spin-1/2 chain using two methods: (a) a homogeneous spin chain with week end bonds and equal Larmor frequencies and (b) a homogeneous spin chain with end Larmor frequencies different from inner ones. A tridiagonal matrix representation of the XY Hamiltonian with nearest neighbor interactions relevant to the quantum state transfer is exactly diagonalized for a combination of the above two methods. In order to take into account interactions of the remote spins we used numerical simulations of the quantum state transfer in ten-node chains. We compare the state transfer times obtained using the two above methods for chains governed by the both XY and XXZ Hamiltonians and using both nearest neighbor and all node interactions.

quant-ph↗