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Journal of Physics A Mathematical and Theoretical

Multiparty-controlled teleportation of an arbitrarym-qudit state with a pure entangled quantum channel

Ping Zhou, Xihan Li, Fu‐Guo Deng, Hong-Yu Zhou

Published Oct 9, 2007• 105 citations
Publisher

Abstract

We present a general scheme for multiparty-controlled teleportation of an arbitrary m -qudit ( d -dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2 m particles, the controllers take some single-particle measurements with the measuring basis X d and the receiver only needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m -qudit state equals the entanglement of the quantum channel.

DOI
10.1088/1751-8113/40/43/019

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提出了一个基于高维2m+1粒子纠缠态的任意m粒子态量子可控离物传态方案,发送方alice对需传送的未知态量子系统和手中的纠缠粒子执行m个广义bell基测量,控制方执行广义x基测量,依据预先共享量子纠缠态非定域相关性,接收方对手中的粒子执行相应的幺正操作就可以重建原来未知量子态.与其他方案相比,方案减少了任意高维多粒子态可控离物传送所需传送粒子数.我们进一步讨论了基于纯纠缠信道的概率量子可控离物传态方案,通过与发送方和控制方合作,接收方只需对手中的纠缠粒子和引入的附加粒子执行联合幺正演化和投影测量,就可以在他的粒子上概率的重建原来的未知量子态,最后,方案计算讨论了基于纯纠缠态量子可控离物传态成功概率与信道纠缠度之间的关系. abstract： a general scheme for controlled teleportation of an arbitrary m-qubit (high-dimensional quantum system) state with a d-dimensional (2m+1)-particle entangled state is presented.the arbitrary m-qubit state can be teleported if the sender (alice) performs m generalized bell state measurements on his particles and the controller (bob) performs single particle generalized xbasis measurement on his particle. the original m-qubit state can be reconstructed on the receiver's particles if the receiver (charlie) performs corresponding unitary operations on his particles according to the measurement results of the sender and the controller.the scheme has the advantage of transmitting much less particles for controlled teleportation of an unknown m-qubit state than others. moreover,the application of the scheme by using a nonmaximally entangled state as its quantum channel is discussed. the original m-qubit state can be probabilistically reconstructed on the receiver's particles if the receiver introduces an auxiliary qubit and performs the general unitary transformation on his entangled particles and the auxiliary qubit.the relationship betwe

ACTA PHOTONICA SINICA•Jan 1, 2012•1 citation
We present a general scheme for multiparty-controlled teleportation of an arbitrary m -qudit ( d -dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2 m particles, the controllers take some single-particle measurements with the measuring basis X d and the receiver only needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m -qudit state equals the entanglement of the quantum channel.
We present a general scheme for multiparty-controlled teleportation of an arbitrary m-qudit (ddd-dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2mmm particles, the controllers take some single-particle measurements with the measuring basis XdX_{d}Xd​ and the receiver only need to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid some a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m-qudit state equals to the entanglement of the quantum channel.
A general scheme for controlled teleportation of an arbitrary multi-qudit state with d -dimensional Greenberger–Horne–Zeilinger (GHZ) states is proposed. For an arbitrary m -qudit state, the sender Alice performs m generalized Bell-state projective measurements on her 2 m qudits and the controllers need only take some single-particle measurements. The receiver Charlie can reconstruct the unknown m -qudit state by performing some single-qudit unitary operations on her particles if she cooperates with all the controllers. As the quantum channel is a sequence of maximally entangled GHZ states, the intrinsic efficiency for qudits in this scheme approaches 100% in principle.
Quantum teleportation is a unique quantum information processing method in quantum communication. Researchers have shown considerable interest in hierarchically controlled teleportation by using quantum entangled states as the quantum channel. Protocols for the hierarchically controlled teleportation of an arbitrary single-qubit via a four-qubit χ state and a four-qubit cluster state have been proposed. We present a protocol for the hierarchically controlled teleportation of an arbitrary m-qudit (d-dimensional quantum system) state by using a partially entangled quantum state as the quantum channel. The sender performs m generalized Bell-state measurements on her 2m particles. To reconstruct the original state, the upper-grade receiver only needs to apply a unitary operation in accordance with one of the receivers’ measurement results, and the lower-grade receivers need to perform a unitary operation according to all the other receivers’ measurement results. The receivers can reconstruct the original state probabilistically by introducing an auxiliary qubit and performing a collective unitary transformation. The protocol has the advantage of having high channel capacity by using a high-dimensional entangled state as the quantum channel.
We first provide four new schemes for two-party quantum teleportation of an arbitrary unknown multi-particle state by using three-, four-, and five-particle states as the quantum channel, respectively. The successful probability and fidelity of the four schemes reach 1. In the first two schemes, the receiver can only apply one of the unitary transformations to reconstruct the original state, making it easier for these two schemes to be directly realized. In the third and fourth schemes, the sender can preform Bell-state measurements instead of multipartite entanglement measurements of the existing similar schemes, which makes real experiments more suitable. It is found that the last three schemes may become tripartite controlled teleportation schemes of teleporting an arbitrary multi-particle state after a simple modification. Finally, we present a new scheme for three-party sharing an arbitrary unknown multi-particle state. In this scheme, the sender first shares three three-particle GHZ states with two agents. After setting up the secure quantum channel, an arbitrary unknown multi-particle state can be perfectly teleported if the sender performs three Bell-state measurements, and either of two receivers operates an appropriate unitary transformation to obtain the original state with the help of other receiver's three single-particle measurements. The successful probability and fidelity of this scheme also reach 1. It is demonstrated that this scheme can be generalized easily to the case of sharing an arbitrary unknown multi-particle state among several agents.
Abstract The purpose of this article is to explore how to transmit low-dimensional unknown single-particle states in a multi-output manner through a high-dimensional entangled state as a quantum channel under the control of a supervisor. First, we construct a set of complete orthogonal non-symmetric bases in ( d × f ) -dimensional Hilbert space and a ( 2 N + 1 ) -qudit maximally entangled state in d -dimensional Hilbert space, taking a set of ( 3 × 2 ) -dimensional non-symmetric bases and a 3-dimensional 5-qutrit entangled state as their special cases, respectively. We then propose a controlled teleportation scheme, where by using the 3-dimensional 5-qutrit maximally entangled state as a quantum channel and employing the ( 3 × 2 ) -dimensional non-symmetric basis measurement, two 2-dimensional single-qubit states are simultaneously teleported through quantum teleportation technology under the control of a supervisor. Subsequently, the above maximally entangled quantum channel is replaced by a 3-dimensional 5-qutrit non-maximally entangled state, and two unknown single-qubit states are teleported, under the control of a supervisor, in such a way that they can be probabilistically reconstructed by introducing auxiliary qubits and performing appropriate operations. The success probabilities of the above two schemes are given, and the analysis shows that the scheme based on a non-maximally entangled channel is a generalization of the previous scheme. In addition, the above schemes can be extended from the following two perspectives: (a) the quantum channels can be extended from 3-dimensional to arbitrary d -dimensional; (b) the transmitted quantum information can be extended from 2-dimensional to any f -dimensional through d -dimensional entangled quantum channels ( f < d ).
提出了一个基于高维2m+1粒子纠缠态的任意m粒子态量子可控离物传态方案,发送方alice对需传送的未知态量子系统和手中的纠缠粒子执行m个广义bell基测量,控制方执行广义x基测量,依据预先共享量子纠缠态非定域相关性,接收方对手中的粒子执行相应的幺正操作就可以重建原来未知量子态.与其他方案相比,方案减少了任意高维多粒子态可控离物传送所需传送粒子数.我们进一步讨论了基于纯纠缠信道的概率量子可控离物传态方案,通过与发送方和控制方合作,接收方只需对手中的纠缠粒子和引入的附加粒子执行联合幺正演化和投影测量,就可以在他的粒子上概率的重建原来的未知量子态,最后,方案计算讨论了基于纯纠缠态量子可控离物传态成功概率与信道纠缠度之间的关系. abstract： a general scheme for controlled teleportation of an arbitrary m-qubit (high-dimensional quantum system) state with a d-dimensional (2m+1)-particle entangled state is presented.the arbitrary m-qubit state can be teleported if the sender (alice) performs m generalized bell state measurements on his particles and the controller (bob) performs single particle generalized xbasis measurement on his particle. the original m-qubit state can be reconstructed on the receiver's particles if the receiver (charlie) performs corresponding unitary operations on his particles according to the measurement results of the sender and the controller.the scheme has the advantage of transmitting much less particles for controlled teleportation of an unknown m-qubit state than others. moreover,the application of the scheme by using a nonmaximally entangled state as its quantum channel is discussed. the original m-qubit state can be probabilistically reconstructed on the receiver's particles if the receiver introduces an auxiliary qubit and performs the general unitary transformation on his entangled particles and the auxiliary qubit.the relationship betwe