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arXiv:quant-ph/0511223 · Journal of Physics B Atomic Molecular and Optical Physics

Efficient symmetric multiparty quantum state sharing of an arbitrarym-qubit state

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

Published Apr 5, 2006• 212 citations
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Abstract

We present a scheme for symmetric multiparty quantum state sharing of an arbitrary m -qubit state with m Greenberger–Horne–Zeilinger states following some ideas from the controlled teleportation (2005 Phys. Rev. A 72 02338). The sender Alice performs m Bell-state measurements on her 2 m particles and the controllers need only take some single-photon product measurements on their photons independently, not multipartite entanglement measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown m -qubit state and it is an optimal one as its efficiency for qubits approaches 100% in principle.

DOI
10.1088/0953-4075/39/8/015

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We present a scheme for symmetric multiparty quantum state sharing of an arbitrary m -qubit state with m Greenberger–Horne–Zeilinger states following some ideas from the controlled teleportation (2005 Phys. Rev. A 72 02338). The sender Alice performs m Bell-state measurements on her 2 m particles and the controllers need only take some single-photon product measurements on their photons independently, not multipartite entanglement measurements, which makes this scheme more convenient than the latter. Also it does not require the parties to perform a controlled-NOT gate on the photons for reconstructing the unknown m -qubit state and it is an optimal one as its efficiency for qubits approaches 100% in principle.
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.
We present a way for symmetric multiparty-controlled teleportation of an arbitrary two-particle entangled state based on Bell-basis measurements by using two Greenberger-Horne-Zeilinger states, i.e., a sender transmits an arbitrary two-particle entangled state to a distant receiver, an arbitrary one of the n+1n+1n+1 agents, via the control of the others in a network. It will be shown that the outcomes in the cases that nnn is odd or is even are different in principle as the receiver has to perform a controlled-NOT operation on his particles for reconstructing the original arbitrary entangled state in addition to some local unitary operations in the former. Also we discuss the applications of this controlled teleporation for quantum secret sharing of classical and quantum information. As all the instances can be used to carry useful information, its efficiency for qubit approaches the maximal value.
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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.
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.