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Chinese Physics Letters

Remote State Preparation with Genuine Multipartite Entanglement

Ma Yi-Cong, Yongsheng Zhang, Guo Guang-Can

Published Feb 19, 2007• 10 citations
Publisher

Abstract

Enlightened by the work of Yeo and Chua [Phys. Rev. Lett. 96 (2006) 060502] for teleportation and dense coding with genuine multipartite entanglement, we present an explicit protocol for faithful remote state preparation in a real coefficient case by using the same four-particle entangled state which is not reducible to pair of Bell states. It is shown that any complex coefficient case can be changed to a real coefficient case. With this protocol, the state can play an analogous role to Einstein–Podolsky–Rosen pairs in the theory of multipartite entanglement.

DOI
10.1088/0256-307x/24/3/006

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Comment on “Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement”

Fu‐Guo Deng

The multipartite state in the Rigolin's protocol [Phys. Rev. A 71, 032303 (2005)] for teleporting an arbitrary two-qubit state is just a product state of $N$ Einstein-Podolsky-Rosen pairs in essence, not a genuine multipartite entangled state, and this protocol in principle is equivalent to the Yang-Guo protocol [Chin. Phys. Lett. 17, 162 (2000)].

Physical Review A•Sep 14, 2005•50 citations
Enlightened by the work of Yeo and Chua [Phys. Rev. Lett. 96 (2006) 060502] for teleportation and dense coding with genuine multipartite entanglement, we present an explicit protocol for faithful remote state preparation in a real coefficient case by using the same four-particle entangled state which is not reducible to pair of Bell states. It is shown that any complex coefficient case can be changed to a real coefficient case. With this protocol, the state can play an analogous role to Einstein–Podolsky–Rosen pairs in the theory of multipartite entanglement.
Recently Yeo and Chua [Phys. Rev. Lett. 96, 060502 (2006)] presented an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entanglement channel. Here we generalize completely their results to teleporting an arbitrary NNN-qubit state via genuine NNN-qubit entanglement channels. And we present the general form of the genuine multipartite entanglement channels, namely, the sufficient and necessary condition the genuine NNN-qubit entanglement channels must satisfy to teleport an arbitrary NNN-qubit state.
由 Yeo 和 Chua 的工作照亮了[Phys。加快。Lett。96 (2006 ) 060502 ] 为远距传物并且与真多国参加的纠纷的稠密的编码，我们在场为在由使用 samefour 粒子的一个真实系数盒子中的忠诚遥远的州的准备的 explicitprotocol 纠缠了不可约贝尔状态配对的状态。anycomplex 系数大小写能被改变到一个真实系数盒子，这被显示出。与这个协议，到 Einstein-Podolsky Rosen 的一个类似的角色在 multipartiteentanglement 的理论配对的 statecan 戏。
In this letter we present an explicit protocol calB2{\\cal B}_2calB2​ for faithfully teleporting an arbitrary 2-qubit state with a class of 4-qubit entangled states. We construct these states in a way different from that of Yeo and Chua [Phys. Rev. Lett. 94, 060502 (2006)]. We will show that the genuine states presented by Yeo and Chua are only a subset of our entangled states. The generalizations of the protocol calB2{\\cal B}_2calB2​ to general protocols calBn{\\cal B}_ncalBn​ and calDn{\\cal D}_ncalDn​, i.e., teleporting an arbitrary nnn-qubit or nnn-qudit state by using the genuine 2n2n2n-qubit or 2n2n2n-qudit entangled states we construct, are also sketched.
We present an explicit protocol E0 for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entangled state. By construction, our four-partite state is not reducible to a pair of Bell states. Its properties are compared and contrasted with those of the four-party Greenberger-Horne-Zeilinger and W states. We also give a dense coding scheme D0 involving our state as a shared resource of entanglement. Both D0 and E0 indicate that our four-qubit state is a likely candidate for the genuine four-partite analogue to a Bell state.
We propose several schemes for the joint remote preparation of four-qubit cluster-type states with real coefficients and complex coefficients by using six Einstein–Podolsky–Rosen (EPR) pairs and two six-qubit entangled states as quantum channels respectively. In these schemes, two senders share the original state which they wish to help the receiver to remotely prepare. It is shown that, only if two senders collaborate with each other, and perform four-qubit projective measurements on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations.
The multipartite state in the Rigolin's protocol [Phys. Rev. A 71, 032303 (2005)] for teleporting an arbitrary two-qubit state is just a product state of NNN Einstein-Podolsky-Rosen pairs in essence, not a genuine multipartite entangled state, and this protocol in principle is equivalent to the Yang-Guo protocol [Chin. Phys. Lett. 17, 162 (2000)].