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arXiv:quant-ph/0005002 · Chinese Physics Letters

Preparation of GHZ States via Grover's Quantum Searching Algorithm

Zeng Hao-Sheng, Kuang Le-Man

Published Jun 1, 2000• 5 citations
arXivHTMLPDF

Abstract

We propose an approach to prepare GHZ (Greenberger, Horne, Zeilinger) states of an arbitrary multi-particle system in terms of Grover's fast quantum searching algorithm. The approach can be used to produce other entangled states with various degrees of entanglement.
DOI
10.1088/0256-307x/17/6/009

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We introduce a class of multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two qubit systems for Bell states and for the class of GHZ states, respectively. We generalize the bi-system entanglement swapping of Bell states and multi-particle GHZ states to any number of qubit systems. We further study the entanglement swapping schemes between any number of Bell states and between any number of the introduced GHZ states in a detailed way, and propose the schemes that can generate two identical GHZ states. We illustrate the applications of such schemes in quantum information processing by proposing quantum protocols for quantum key distribution, quantum secret sharing and quantum private comparison.
We propose to employ the amplification mechanism of Grover's search algorithm to efficiently prepare entangled states of an ensemble of qubits. The conditional change of sign employed in the algorithm can be implemented by the phase shift of photons scattered on an optical cavity hosting an atomic ensemble. We show that collective Dicke states, Greenberger-Horne-Zeilinger states, and Schrödinger cat superpositions of N atoms may be prepared deterministically by few (∼N^{1/4}) photon scattering events without individual addressing of the atoms.
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.
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