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arXiv:quant-ph/0504158 · Physical Review A

Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs

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

Published Oct 5, 2005• 462 citations
arXivHTMLPDF

Abstract

A scheme for multiparty quantum state sharing of an arbitrary two-particle state is presented with Einstein-Podolsky-Rosen pairs. Any one of the $N$ agents has the access to regenerate the original state with two local unitary operations if he collaborates with the other agents, say the controllers. Moreover, each of the controllers is required to take only a product measurement ${\ensuremath{\sigma}}_{x}\ensuremath{\bigotimes}{\ensuremath{\sigma}}_{x}$ on his two particles, which makes this scheme more convenient for the agents in the applications on a network than others. As all the quantum source can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. With a new notation for the multipartite entanglement, the sender need only publish two bits of classical information for each measurement, which reduces the information exchanged largely.

DOI
10.1103/physreva.72.044301

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We present an efficient scheme for sharing an arbitrary m-qubit state with n agents. In our scheme, the sender Alice first shares m Bell states with the agent Bob, who is designated to recover the original m-qubit state. Furthermore, Alice introduces n − 1 auxiliary particles in the initial state |0⟩, applies Hadamard (H) gate and Controlled-Not (CNOT) gate operations on the particles, which make them entangled with one of m particle pairs in Bell states, and then sends them to the controllers (i.e., other n − 1 agents), where each controller only holds one particle in hand. After Alice performing m Bell-basis measurements and each controller a single-particle measurement, the recover Bob can obtain the original unknown quantum state by applying the corresponding local unitary operations on his particles. Its intrinsic efficiency for qubits approaches 100%, and the total efficiency really approaches the maximal value.
In this paper, we propose a scheme where Alice shares an arbitrary m-particle unknown state with her agents, Bob and Charlie. Alice starts by distributing 2m Einstein–Podolsky–Rosen pairs with her agents and performs m joint three-particle Greenberger–Horne–Zeilinger state measurements on her particles. Bob, who acts as the controller, performs a product measurement [Formula: see text] on his m qubit states while Charlie retrieves the original state by performing unitary operations on his m particles. Subsequently, we demonstrate our proposed scheme’s feasibility by applying it in electronic voting by sharing an arbitrary single-particle state.
A theoretical scheme for multiparty multi-particle state sharing is proposed. After she introduces auxiliary particles and Einstein–Podolsky–Rosen (EPR) pairs, the sender (Alice) performs Hadamard (H) gate operations and Controlled-NOT (CNOT) gate operations on them. Subsequently, the sender leaves one particle sequence and distributes the rest particles to the other participants. And then, the sender makes Bell-state measurements on her particles and publishes the measurement outcomes via the classical channel to realize the quantum state sharing among the others. Only the simple operations are used to realize quantum state sharing. The sender may increase or decrease the number of the participants by changing the number of the auxiliary particles.
We propose a scheme for sharing an arbitrary unknown two-qubit state among three parties by using a four-qubit cluster-class state and a Bell state as a quantum channel. With a quantum controlled phase gate (QCPG) operation and a local unitary operation, any one of the two agents has the access to reconstruct the original state if he/she collaborates with the other one, whilst individual agent obtains no information. As all quantum resource can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. Moreover, the present scheme is more feasible with present-day technique.
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