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International Journal of Quantum Information

QUANTUM STATE SPLITTING WITH YEO–CHUA GENUINE ENTANGLED STATE

Yimin Liu, Wen Zhang, Xueqin Zuo, Zhanjun Zhang

Published Sep 1, 2010• 6 citations
Publisher

Abstract

Utilizing the four-qubit genuine entangled state presented by Yeo and Chua [Phys. Rev. Lett.96 (2006) 060502], we propose a tripartite quantum state splitting scheme for a sender to achieve the bipartition of his/her arbitrary two-qubit pure state between two sharers. During the scheme design, two novel and important ideas originated, respectively, from Phys. Rev. A74 (2006) 054303 and J. Phys. B41 (2008) 145506 are adopted to enhance the security and optimize resource consumption, operation complexity, and intrinsic efficiency. In the scheme, first the sender performs two Bell-state measurements and publishes the results. Afterwards, if and only if the two sharers cooperate together, they can perfectly restore the sender's quantum pure state by executing first a two-qubit collective unitary operation and then two single-qubit unitary operations.

DOI
10.1142/s0219749910006757

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Utilizing the four-qubit genuine entangled state presented by Yeo and Chua [Phys. Rev. Lett.96 (2006) 060502], we propose a tripartite quantum state splitting scheme for a sender to achieve the bipartition of his/her arbitrary two-qubit pure state between two sharers. During the scheme design, two novel and important ideas originated, respectively, from Phys. Rev. A74 (2006) 054303 and J. Phys. B41 (2008) 145506 are adopted to enhance the security and optimize resource consumption, operation complexity, and intrinsic efficiency. In the scheme, first the sender performs two Bell-state measurements and publishes the results. Afterwards, if and only if the two sharers cooperate together, they can perfectly restore the sender's quantum pure state by executing first a two-qubit collective unitary operation and then two single-qubit unitary operations.
A four-party single-qubit operation sharing scheme is put forward by utilizing the Bell and Yeo–Chua product state in an entanglement structure as the composite quantum channel. Four features of the scheme are discussed and confirmed, including its determinacy, symmetry, and security as well as the scheme experimental feasibility. Moreover, some concrete comparisons between our present scheme and a previous scheme [H. Xing et al., Quantum Inf. Process. 13 (2014) 1553] are made from the aspects of quantum and classical resource consumption, necessary operation complexity, and intrinsic efficiency. It is found that our present scheme is more superior than that one. In addition, the essential reason why the employed state in the entanglement structure is applicable for sharing an arbitrary single-qubit operation among four parties is revealed via deep analyses. With respect to the essential reason, the capacity of the product state in quantum operation sharing (QOS) is consequently shown by simple presenting the corresponding schemes with the state in other entanglement structures.
We propose two schemes for splitting single- and two-qubit states by using four-particle genuine entangled state as the quantum channel. After the sender performs Bell-basis (or three-partite GHZ- basis) measurements on her particles, and the cooperators operate single-particle measurements on their particles, the state receiver can reconstruct the original state of the sender by applying the appropriate unitary operation. In particular, in the scheme for splitting two-qubit state, the receiver needs to introduce an auxiliary particle and carries out a C-NOT operation.
A three-party scheme for sharing an arbitrary single-qubit operation on a distant target qubit is proposed by first utilizing a six-qubit genuinely entangled state presented by [Borras et al., J. Phys. A 40, 13407 (2007)]. The security of the scheme is simply analyzed and ensured. The essential role which the state in the given qubit distribution plays in the QOS task is revealed. The important features including the sharing determinacy and the sharer symmetry are identified. Moreover, the experimental implementation feasibility of the scheme is discussed and confirmed.
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.
Through introducing the new application of a genuinely entangled six-qubit state,quantum information splitting of an arbitrary two-qubit state was investigated.For the quantum information splitting,a genuinely entangled six-qubit state was shared by a sender(Alice),a controller(Charlie) and a receiver(Bob).The sender firstly performed twice Bell-state measurements,and then the controller made a Bell-state measurement.Finally the receiver can reconstruct the arbitrary two-qubit state by performing some appropriate unitary transformations on his qubits after he knew the measured results of both the sender and the controller.This quantum information splitting scheme is deterministic,i.e.the probability of success is 100%.In comparison with the quantum information splitting scheme using the same quantum channel the sender and the controller only need to perform Bell-state measurements,not joint multi-qubit measurement,which makes this scheme simpler and easier,and can be fulfilled based on present experimental technology.
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.