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arXiv:1701.03585 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum entanglement and quantum discord in dimers in multiple quantum NMR experiments

S. A. Gerasev, E. I. Kuznetsova

Published Dec 30, 2016• 1 citation
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Abstract

Quantum correlations in multiple quantum (MQ) NMR experiments are investigated in two-spin systems (dimers). In the initial moment of time one spin is in a pure quantum polarized state and the other spin is in the thermodynamic equilibrium state defined by the temperature of the sample. MQ NMR dynamics of dimers is investigated. It is shown that MQ NMR coherences of only the zeroth and second orders emerge in such a system. The intensities of those coherences are calculated. Entangled states appear in the course of the system evolution in the MQ NMR experiment. The quantum discord is obtained in the high temperature approximation.

DOI
10.1117/12.2264353

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Quantum correlations in multiple quantum (MQ) NMR experiments are investigated in two-spin systems (dimers). In the initial moment of time one spin is in a pure quantum polarized state and the other spin is in the thermodynamic equilibrium state defined by the temperature of the sample. MQ NMR dynamics of dimers is investigated. It is shown that MQ NMR coherences of only the zeroth and second orders emerge in such a system. The intensities of those coherences are calculated. Entangled states appear in the course of the system evolution in the MQ NMR experiment. The quantum discord is obtained in the high temperature approximation.
In this work, quantum correlations in two model systems which can be invesitgated by means of solid-state NMR are considered. The first is a two-spin system in NMR spin-locking experiment, where two schemes of spin-locking are considered. Concurrence is calculated for both schemes assuming the initial thermodynamic equilibrium state. Quantum discord is calculated analytically in the high-temperature approximation. The second model system is the spin-1/2 chain with the XY interaction, where the transfer of multiple quantum (MQ) coherences from one end of the chain to another is studied. The conditions under which the density matrix of the receiver is a block-scaled version of the sender’s density matrix are found.
We investigate the evolution of entanglement in multiple-quantum (MQ) NMR experiments in crystals with pairs of close nuclear 1/2-spins. The initial thermodynamic equilibrium state of the system in a strong external magnetic field evolves under the nonsecular part of the dipolar Hamiltonian. As a result, MQ coherences of the zeroth and plus/minus second orders appear. A simple condition for the emergence of entanglement is obtained. We show that the measure of the spin-pair entanglement—concurrence—coincides qualitatively with the intensity of MQ coherences of the plus/minus second order and, hence, the entanglement can be studied with MQ NMR methods. We introduce an entanglement witness using MQ NMR coherences of the plus/minus second order.
The dynamics of entanglement is investigated on the basis of exactly solvable models of multiple quantum (MQ) NMR spin dynamics. It is shown that the time evolution of MQ coherences of systems of coupled nuclear spins in solids is directly connected with dynamics of the quantum entanglement. We studied analytically the dynamics of entangled states for two- and three-spin systems coupled by the dipole-dipole interaction. In this case the dynamics of the quantum entanglement is uniquely determined by the time evolution of MQ coherences of the second order. The real part of the density matrix describing MQ dynamics in solids is responsible for MQ coherences of the zeroth order while its imaginary part is responsible for the second order. Thus, one can conclude that the dynamics of the entanglement is connected with transitions from the real part of the density matrix to the imaginary one, and vice versa. A pure state which generalizes the Greenberger-Horne-Zeilinger (GHZ) and W states is found. Different measures of the entanglement of this state are analyzed for tripartite systems.
We propose the algorithm for the quantum computer on the IBM Q platform. By this algorithm one can obtain the multiple-quantum NMR dynamics of the dimer with spins 1/2. Our algorithm includes preparation of thermodynamic equilibrium state as initial conditions for dimer and circuit for evolution under the Hamiltonian of multiple-quantum NMR experiment. Multiple-quantum coherences arise in multiple-quantum NMR experiment. Ones are connected with solid body structure and get a lot of research consequently. Intensities of these coherences are measured at end of experiment. In our algorithm the intensities of multiple-quantum coherences are evaluated by tomography of diagonal elements of final density matrix for dimer.
We investigated dynamics of entangled states on the basis of multiple-quantum (MQ) NMR methods. A time evolution of MQ coherences of nuclear spins coupled by the dipole-dipole interactions (DDI) in solids is simply connected with dynamics of quantum entangled states. We studied analytically dynamics of the entangled states for two- and three-spin systems. In this case dynamics of the quantum entanglement is uniquely determined by the time evolution of MQ coherences of the second order. The real part of the density matrix describing MQ dynamics in solids is responsible for MQ coherences of the zeroth order while its imaginary part is responsible for the second order. Thus, one can conclude that dynamics of the entanglement is connected with transitions from the real part of the density matrix to the imaginary one and vice versa.
We use multiple quantum (MQ) nuclear magnetic resonance dynamics of a gas of spin-carrying molecules in nanocavities at high and low temperatures for an investigation of many-particle entanglement. A distribution of MQ NMR intensities is obtained at high and low temperatures in a system of 201 spins 12\frac{1}{2}21​. The second moment of the distribution, which provides a lower bound on the quantum Fisher information, sheds light on the many-particle entanglement in the system. The dependence of the many-particle entanglement on the temperature is investigated. Almost all spins are entangled at low temperatures.