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Register a new userMultiple-Quantum Spin Dynamics of Entanglement
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Added by
Serge Ivanovich Doronin
Publication date
2003
fields
Physics
and research's language is
English
Authors
S. I. Doronin
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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.
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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.
Dymanics of spin dimers in multiple quantum NMR experiment is studied on the 5-qubit superconducting quantum processor of IBM {Quantum Experience} for the both {pure} ground and thermodynamic equilibrium (mixed) initial states. The work can be considered as a first step towards an application of quantum computers to solving problems of magnetic resonance. This article is dedicated to Prof. Klaus Mobius and Prof. Kev Salikhov on the occasion of their 85th birthdays.
Quantum simulation of spin models can provide insight into complex problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. Here we study non-equilibrium, quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of $^9$Be$^+$ ions in a Penning trap. We verify entanglement in the form of spin-squeezed states for up to 219 ions, directly observing 4.0$pm$0.9 dB of spectroscopic enhancement. We also observe evidence of non-Gaussian, over-squeezed states in the full counting statistics. We find good agreement with ab-initio theory that includes competition between entanglement and decoherence, laying the groundwork for simulations of the transverse-field Ising model with variable-range interactions, for which numerical solutions are, in general, classically intractable.
Multiple quantum (MQ) NMR with a dipolar ordered initial state opens new possibilities for the exploration of many-spin entanglement. In this paper, we investigate many-spin entanglement in a gas of spin-carrying molecules (atoms) in nanocavities in the conditions of MQ NMR with a dipolar ordered initial state. The second moment of the distribution of the intensities of MQ NMR coherences, which provides a lower bound on the quantum Fisher information, is used for an estimate of the number of the entangled spins. Many-spin entanglement is investigated at different temperatures and different numbers of spins.
A new entanglement measure, the multiple entropy measures (MEMS), is proposed to quantify quantum entanglement of multi-partite quantum state. The MEMS is vector-like with $m=[N/2]$, the integer part of $N/2$, components: $[S_1, S_2,..., S_m]$, and the $i$-th component $S_i$ is the geometric mean of $i$-body partial entropy of the system. The $S_i$ measures how strong an arbitrary $i$ bodies from the system are entangled with the rest of the system. The MEMS is not only transparent in physical picture, but also simple to calculate. It satisfies the conditions for a good entanglement measure. We have analyzed the entanglement properties of the GHZ-state, the W-states and cluster-states under MEMS. The cluster-state is more entangled than the GHZ-state and W-state under MEMS.
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