Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments

Abstract

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.

arXiv comment5 pages, 2 figures

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• Many-particle Entanglement in Multiple Quantum NMR Spectroscopy
• Entanglement detection on an NMR quantum information processor using random local measurements
• Entanglement witnesses in the XY chain: Thermal equilibrium and postquench nonequilibrium states
• Entanglement in nuclear quadrupole resonance
• Fading entanglement near equilibrium state
• PULSEE: A software for the quantum simulation of an extensive set of magnetic resonance observables
• Many-spin entanglement in multiple quantum NMR with a dipolar ordered initial state
• Quantum entanglement and quantum discord in dimers in multiple quantum NMR experiments