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International Journal of Quantum Information

A QUANTUM SPLITTING SCHEME OF ARBITRARY TWO-QUBIT STATE USING FOUR-QUBIT CLUSTER STATE

Guixia Pan, Yimin Liu, Xiaofeng Yin, Wen Zhang, Zhanjun Zhang

Published Oct 1, 2008• 13 citations
Publisher

Abstract

In this paper, we explore the channel capacity of the 4-qubit 4-term cluster state (i.e. (|0000〉 + |0011〉 + |1100〉 - |1111〉)/2) for splitting arbitrary two-qubit quantum information. After our extensive investigations, we found that 4 out of 12 possible distributions of the 4 qubits can be utilized to realize bipartite splitting. In terms of each distribution, the corresponding splitting scheme is presented and LOCCs (local operation and classical communication) are explicitly given.

DOI
10.1142/s021974990800433x

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In this paper, we explore the channel capacity of the 4-qubit 4-term cluster state (i.e. (|0000〉 + |0011〉 + |1100〉 - |1111〉)/2) for splitting arbitrary two-qubit quantum information. After our extensive investigations, we found that 4 out of 12 possible distributions of the 4 qubits can be utilized to realize bipartite splitting. In terms of each distribution, the corresponding splitting scheme is presented and LOCCs (local operation and classical communication) are explicitly given.
The theory of an experimentally feasible four-partite scheme for splitting and open-destination teleportation of an arbitrary two-qubit state is presented. In this scheme, the quantum channel is provided by a pair of four-qubit generalized (G) Bell-states, which are decomposable. We show that not all possible distributions of entangled qubits to four communicating parties result in successful open-destination teleportation. We theoretically prove that two Bell-state measurements performed by a sender result in splitting, distributing, and locking the two-qubit state among three different receivers. The complete details of the procedure for unlocking the shared two-qubit state and eventually regenerating it at the location of any one of the three receiving stations is theoretically analyzed. This unlocking and regeneration procedure consists of local operations and classical communication (LOCC) performed by the remaining two receivers.
Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements, and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement (POVM) instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.
In this study, we have proposed a scheme for two-way quantum communication in which the two legitimate participants mutually exchange their quantum information to each other by using a four-qubit cluster state as the quantum channel. Recently, by utilizing four-qubit cluster state as the quantum channel, Kazemikhah et al. [Int. J. Theor. Phys. 60, 378 (2021)] tried to design a scheme for mutual exchange of quantum information between two legitimate participants. However, in this study, it has been shown that in their scheme, the transmission of quantum information cannot be realized because the two participants are not entangled to each other due to a trivial conceptual mistake made by Kazemikhah et al. in the description of the quantum channel. Here, we have shown that two legitimate participants can teleport quantum information states to each other by using four-qubit cluster state as the quantum channel, provided they co-operate with each other and perform nonlocal controlled phase gate operation. If both participants do not co-operate with each other, then no one can reconstruct the information sent to them, and therefore, the exchange of information is possible only when both participants are honest to each other.
A scheme of using four-qubit cluster state as quantum channel(QC)to convey the quantum state information is proposed to realize two-way communication.In this scenario,two sides of communication,Alice and Bob,share a four-qubit cluster state.In the process of communication,at first,four-qubit cluster state form a whole system with quantum state information two sides have.Then,Alice and Bob perform Bell-state joint measurements to their own part qubits respectively,and tell the measured results to each other via classical channel(CC).Finally,according to the measured results,Alice and Bob make corresponding unitary transformations,hence its own party can reappear the opposite quantum state information.So two-way communication of quantum state information is achieced.