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Chinese Science Bulletin

An efficient scheme for multi-party quantum state sharing via non-maximally entangled states

Min Jiang, Xu Huang, Liulei Zhou, YiMing Zhou, Jia Zeng

Published Mar 20, 2012• 14 citations
Publisher

Abstract

We present a new scheme for investigating the usefulness of non-maximally entangled states for multi-party quantum state sharing in a simple and elegant manner. In our scheme, the sender, Alice shares n various probabilistic channels composed of non-maximally entangled states with n agents in a network. Our protocol involves only Bell-basis measurements, single qubit measurements, and a two-qubit unitary transformation operated by free optional agents. Our scheme is a more convenient realization because no other multipartite joint measurements are needed. Furthermore, in our scheme various probabilistic channels lessen the requirement for quantum channels, which makes it more practical for physical implementation.

DOI
10.1007/s11434-012-5008-3

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We present a new scheme for investigating the usefulness of non-maximally entangled states for multi-party quantum state sharing in a simple and elegant manner. In our scheme, the sender, Alice shares n various probabilistic channels composed of non-maximally entangled states with n agents in a network. Our protocol involves only Bell-basis measurements, single qubit measurements, and a two-qubit unitary transformation operated by free optional agents. Our scheme is a more convenient realization because no other multipartite joint measurements are needed. Furthermore, in our scheme various probabilistic channels lessen the requirement for quantum channels, which makes it more practical for physical implementation.
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In this paper we present a new scheme for quantum state sharing of an arbitrary unknown two-qubit state by using a non-maximally five-qubit cluster state as quantum channel. In this scheme, the non-maximally five-qubit cluster state is shared by a sender (Alice), a controller (Charlie), and a receiver (Bob), who does not need to introduce an auxiliary particle but only operates an appropriate unitary transformation. The sender introduces an auxiliary particle and makes orthogonal complete bases measurement, and the controller makes a single-particle projective measurement on his particle, then the quantum state sharing can be probabilistically realized.
A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled 丨X） state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice＇s secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.
A scheme that probabilistically realizes hierarchical quantum state sharing of an arbitrary unknown qubit state with a four-qubit non-maximally entangled |χ〉 state is presented in this paper. In the scheme, the sender Alice distributes a quantum secret with a Bell-state measurement and publishes her measurement outcomes via a classical channel to three agents who are divided into two grades. One agent is in the upper grade, while the other two agents are in the lower grade. Then by introducing an ancillary qubit, the agent of the upper grade only needs the assistance of any one of the other two agents for probabilistically obtaining the secret, while an agent of the lower grade needs the help of both the other two agents by using a controlled-NOT operation and a proper positive operator-valued measurement instead of the usual projective measurement. In other words, the agents of two different grades have different authorities to reconstruct Alice's secret in a probabilistic manner. The scheme can also be modified to implement the threshold-controlled teleportation.
By using a proper positive operator-valued measure (POVM), we present a new scheme for probabilistically implementing quantum state sharing of an arbitrary unknown two-qubit state with two non-maximally entangled three-qubit states. In this paper, the sender Alice averagely partitions its unknown original state with two Bell-state measurements and publishes her measurement results via a classical channel. Then by performing a proper POVM, it is shown that either of the two agents Bob or Charlie can recover the original state in a probabilistic manner provided that he/she gets another one's help. Lastly, we concisely generalize the tripartite scheme to a multi-party case.