33 research outputs found
Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments
We investigate the evolution of entanglement in multiple-quantum (MQ) NMR
experiments in crystals with pairs of close nuclear spins-1/2. The initial
thermodynamic equilibrium state of the system in a strong external magnetic
field evolves under the non-secular 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.Comment: 5 pages, 2 figure
Simulations of Quantum Logic Operations in Quantum Computer with Large Number of Qubits
We report the first simulations of the dynamics of quantum logic operations
with a large number of qubits (up to 1000). A nuclear spin chain in which
selective excitations of spins is provided by the gradient of the external
magnetic field is considered. The spins interact with their nearest neighbors.
We simulate the quantum control-not (CN) gate implementation for remote qubits
which provides the long-distance entanglement. Our approach can be applied to
any implementation of quantum logic gates involving a large number of qubits.Comment: 13 pages, 15 figure
Multiple-Quantum Spin Dynamics of Entanglement
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 dynamics of entangled states for two- and three-spin systems
coupled by the dipole-dipole interaction. 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. A pure state which
generalizes the GHZ and W states is found. Different measures of the
entanglement of this state are analyzed for three-partite systems.Comment: 11 pages, 4 figure