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Physical Review A

Efficient scheme for multipartite entanglement and quantum information processing with trapped ions

Wen‐Xing Yang, Zhiming Zhan, Jiahua Li

Published Dec 7, 2005• 75 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.72.062108

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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.
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.
In the system with two two-level ions confined in a linear trap, this paper presents a simple scheme to realize the quantum phase gate (QPG) and the swap gate beyond the Lamb–Dicke (LD) limit. These two-qubit quantum logic gates only involve the internal states of two trapped ions. The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers. Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme. Thus the scheme is simple and the interaction time is very short, which is important in view of decoherence. The experimental feasibility for achieving this scheme is also discussed.
Following the recent proposal by Briegel et al. [Phys. Rev. Lett. 86 (2001) 910], a procedure is proposed for one-step realizing quantum control phase gates with two trapped ions in thermal motion. It is shown that the scheme can also be used to create a new special type of entangled states, i.e., cluster states of many trapped ions. In the scheme the two-trapped ions are simultaneously excited by a single laser beam and the frequency of the laser beam is slightly off resonance with the first lower vibration sideband of the trapped ions. The distinct advantage of the scheme is that it does not use the vibrational mode as the data bus. Furthermore, our scheme is insensitive to both the initial motional state and heating (or decay) as long as the system remains in the Lamb–Dicke regime.
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.