Global Control Methods for GHZ State Generation on 1-D Ising Chain

TL;DR

This paper explores methods for generating GHZ entangled states in a 1-D Ising chain using only global control fields, applicable to various quantum systems, and compares different control strategies under realistic conditions.

Contribution

It introduces a global control approach for GHZ state preparation on an Ising chain and compares three control strategies considering practical imperfections.

Findings

GHZ states can be asymptotically reached from simple initial states.

Finite-time reachability is possible under certain conditions.

Control strategies vary in robustness to imperfections.

Abstract

We discuss how to prepare an Ising chain in a GHZ state using a single global control field only. This model does not require the spins to be individually addressable and is applicable to quantum systems such as cold atoms in optical lattices, some liquid- or solid-state NMR experiments, and many nano-scale quantum structures. We show that GHZ states can always be reached asymptotically from certain easy-to-prepare initial states using adiabatic passage, and under certain conditions finite-time reachability can be ensured. To provide a reference useful for future experimental implementations three different control strategies to achieve the objective, adiabatic passage, Lyapunov control and optimal control are compared, and their advantages and disadvantages discussed, in particular in the presence of realistic imperfections such as imperfect initial state preparation, system inhomogeneity and dephasing.