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Chinese Journal of Quantum Electronics

Simple schemes for preparation of multipartite entangled states of trapped ions

Feng Zhong

Published Jan 1, 2011• 0 citations

Abstract

Three experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions.In the first scheme,a GHZ state can be simply synthesized in a single step. The second scheme is to prepare fully symmetric W states with two steps.The third scheme describes the sequential generation of linear cluster states.In addition,a method to create a larger cluster state was also presented by fuzing the end qubits of two smaller cluster states in order to decrease the distortion caused by decoherence,which can speed up the generation of large cluster states.The above schemes involve the collective interaction between multiple ions with the vibrational ground state and a large detuned laser. Compared with previous schemes,the above schemes have four advantages.Firstly,they do not require the vibrational mode of ions as memory.Secondly,they do not need to address the ions individually.Thirdly, they are free from the effects of phase fluctuation of laser field.Finally,they need less operations.

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Three experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions.In the first scheme,a GHZ state can be simply synthesized in a single step. The second scheme is to prepare fully symmetric W states with two steps.The third scheme describes the sequential generation of linear cluster states.In addition,a method to create a larger cluster state was also presented by fuzing the end qubits of two smaller cluster states in order to decrease the distortion caused by decoherence,which can speed up the generation of large cluster states.The above schemes involve the collective interaction between multiple ions with the vibrational ground state and a large detuned laser. Compared with previous schemes,the above schemes have four advantages.Firstly,they do not require the vibrational mode of ions as memory.Secondly,they do not need to address the ions individually.Thirdly, they are free from the effects of phase fluctuation of laser field.Finally,they need less operations.

Two experimentally feasible schemes are proposed for generating multipartite entangled states of cold trapped ions. In the first scheme, a Greenberger-Horne-Zeilinger state can be simply synthesized in a single step, in view of decoherence mechanism, a reduction of the number of operations for the state preparation is crucial. What’s more, only one laser beam is required in our scheme. The second scheme is to prepare canonical (fully symmetric) W states by two steps. However, in the paper [HÄaner H, HÄansel W, Roos C F, et al. Nature, 2005, 438:643-646.] M steps were required for generating the same W states.

We propose two schemes to prepare entanglement for the vibronic collective states of multiple trapped ions. The first scheme aims to generating multipartite entanglement for vibrational modes of trapped ions, which only requires a single laser beam tuned to the ionic carrier frequency. Our scheme works in the mediated excitation regime, in which the corresponding Rabi frequency is equal to the trap frequency. Beyond their fundamental importance, these states may be of interest for experimental studies on decoherence since the present scheme operates in a fast way. The second scheme aims to preparing the continuous variable multimode maximally Greenberger–Horne–Zeilinger state. The distinct advantage is that the operation time is only limited by the available laser intensity, not by the inherent mechanisms such as off-resonant excitations. This makes it promising to obtain entanglement of multiple coherent and squeezing states with desired amplitudes in a reasonable time.

A simple and scalable scheme is proposed to generate a n-qubit W state in a trapped-ion system without the Lamb–Dicke limit. The n-qubit W state can be generated by the interaction between the ions and the laser field if the collective mode is initially prepared in the single-phonon state and each ion is in the ground state. The scheme only requires a single laser and avoids laser manipulation of the individual ion. The time required to complete the process decreases with the number of ions. The present scheme is not limited to small values of the LD parameter, which greatly enhances operation speeds.

We propose to implement a highly entangled cluster state (HECS) with only one step based on the resonant interactions among N two-level ions and two different standing-wave lasers with a phase difference of π/2. The time for preparation of the HECS is related only to the frequency of the vibrational mode ν (i.e. t=2π/ν). We can ensure that the preparation time is short enough by setting the larger vibrational mode frequency ν to neglect the effect of the decoherence of the qubits. During the process of preparing the HECS, the heating effect of the vibrational mode can be neglected and the initial qubits need only one evolution with the time interval t. The reduced operation steps and the shorter preparation time make the present scheme more feasible in experiments.

In this paper, based on the recent experiment by Roos et al. [Science 304, 1478 (2004)], a theoretical scheme is proposed to create the multipartite entanglement of many trapped ions and implement a two-qubit quantum phase gate between two ions in ion trap. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. We also show that the scheme can be used to directly transfer information between two ions. The scheme has the advantage that it does not use the vibrational mode as the data bus and only requires a single resonant interaction. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed. In view of the decoherence mechanism, the simplification for the entangled state preparation and experimental implementation of quantum logic operation may become crucial.