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arXiv:1004.2589 · Physical Review A

Global control methods for Greenberger-Horne-Zeilinger-state generation on a one-dimensional Ising chain

Xiaoting Wang, Abolfazl Bayat, Sougato Bose, S. G. Schirmer

Published Jul 26, 2010• 32 citations
arXivHTMLPDF

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 nanoscale 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.

DOI
10.1103/physreva.82.012330

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Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and WWW states are two inequivalent classes of multipartite entangled states which cannot be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and WWW states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the WWW state, we find a standard way to prepare the WWW state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.
Greenberger-Horne-Zeilinger (GHZ) state is a typical maximally entangled state which is pursued in both fundamental research and emerging quantum technologies. Preparing large-scale GHZ states in lattice spin systems is particularly appealing for quantum advantages, but conventional schemes face great challenges in scalability. Here we propose a universal and scalable scheme to generate large-scale GHZ-like states, which share similar entanglement and metrological properties with standard GHZ states, in lattice spin systems through global Floquet engineering. Our scheme requires only global operations and shows great advantage for large particle number. It is applicable to systems with arbitrary interaction ranges, offering a practical pathway for large-scale implementation of many-body entangled states in various systems.
Abstract A protocol for generating Greenberger‐Horne‐Zeilinger states in a system of coupled qubits is proposed. The Hamiltonian model assumes ‐wise interactions between the qubits and the presence of a controllable time‐dependent field acting upon one spin only. The dynamical problem is exactly solved thanks to the symmetries of the Hamiltonian model. The possibility of generating GHZ states simulating our physical scenario under both adiabatic and non‐adiabatic conditions is within the reach of the experimentalists. This aspect is discussed in detail.
We propose a method for quantum state transfer in spin chains using an adiabatic passage technique. Modifying even and odd nearest-neighbour couplings in time allows transfer fidelities arbitrarily close to one to be achieved, without the need for precise control of coupling strengths and timing. We study in detail transfer by adiabatic passage in a spin-1 chain governed by a generalized Heisenberg Hamiltonian. We consider optimization of the transfer process applying optimal control techniques. We discuss a realistic experimental implementation using cold atomic gases confined in deep optical lattices.