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SCIENCE CHINA Information Sciences, Volume 64 , Issue 6 : 162302(2021) https://doi.org/10.1007/s11432-020-2977-x

Multi-party blind quantum computation protocol with mutual authentication in network

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  • ReceivedMay 14, 2020
  • AcceptedJul 1, 2020
  • PublishedApr 2, 2021

Abstract


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61671087, 61962009, 61003287), Huawei Technologies Co. Ltd. (Grant No. YBN2020085019), and the Fund of the Fundamental Research Funds for the Central Universities (Grant No. 2019XD-A02).


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  • Figure 1

    Flow chart of three phases in the proposed protocol.

  • Figure 2

    Information flow of each step in registration phase.

  • Figure 3

    Information flow of each step in mutual identity authentication phase.

  • Table 1  

    Table 1Distribution probabilities of CA's Bell-basis measurement results (BMR) and single photons' states $|\gamma\rangle_{A}|\gamma\rangle_{B}$

    $\left|\phi^{+}\right\rangle_{A~B}$ $\left|\phi^{-}\right\rangle_{A~B}$ $\left|\psi^{+}\right\rangle_{A~B}$ $\left|\psi^{-}\right\rangle_{A~B}$
    $|0\rangle_{A}|0\rangle_{B}$ 1/2 1/2 0 0
    $|0\rangle_{A}|1\rangle_{B}$ 0 0 1/2 1/2
    $|1\rangle_{A}|0\rangle_{B}$ 0 0 1/2 1/2
    $|1\rangle_{A}|1\rangle_{B}$ 1/2 1/2 0 0
    $|+\rangle_{A}|+\rangle_{B}$ 1/2 0 1/2 0
    $|+\rangle_{A}|-\rangle_{B}$ 0 1/2 0 1/2
    $|-\rangle_{A}|+\rangle_{B}$ 0 1/2 0 1/2
    $|-\rangle_{A}|-\rangle_{B}$ 1/2 0 1/2 0
  • Table 2  

    Table 2Correlation of CA's non-orthogonal states and $A_{i}$'s & $B_{i~\boldsymbolod~n}$'s measurement results

    $|0\rangle_{B}$ $|1\rangle_{B}$ $|+\rangle_{B}$ $|-\rangle_{B}$
    $|0\rangle_{A}$ $\left|\phi^{-}\right\rangle_{A~B}$ $\left|\psi^{+}\right\rangle_{A~B}$ $\left|\Psi^{+}\right\rangle_{A~B}$ $\left|\Phi^{-}\right\rangle_{A~B}$
    $|1\rangle_{A}$ $\left|\psi^{+}\right\rangle_{A~B}$ $\left|\phi^{-}\right\rangle_{A~B}$ $\left|\Phi^{-}\right\rangle_{A~B}$ $\left|\Psi^{+}\right\rangle_{A~B}$
    $|+\rangle_{A}$ $\left|\Psi^{+}\right\rangle_{A~B}$ $\left|\Phi^{-}\right\rangle_{A~B}$ $\left|\psi^{+}\right\rangle_{A~B}$ $\left|\phi^{-}\right\rangle_{A~B}$
    $|-\rangle_{A}$ $\left|\Phi^{-}\right\rangle_{A~B}$ $\left|\Psi^{+}\right\rangle_{A~B}$ $\left|\phi^{-}\right\rangle_{A~B}$ $\left|\psi^{+}\right\rangle_{A~B}$
  • Table 3  

    Table 3Comparison between our proposed protocol and other BQC protocols

    Our multi-party
    protocol
    Single-server
    protocol [24]
    Single-server
    protocol [26]
    Double-server
    protocol [31]
    Triple-server
    protocol [4]
    Client's capability
    Only measuring states
    Only measuring states
    Preparing states
    Classical
    Preparing states
    Server's capability
    Preparing states
    Preparing states
    Measuring states
    Measuring states
    Measuring states
    Server's number
    $n$ One One
    Two
    Three
    Third party
    Semi-honest None Trusted Trusted None
    Resources states
    Any universal resource state
    Brickwork state
    Brickwork state
    Hyperentangled state
    Bell states
    Extra features
    Identity authentication,
    multi-party
    None
    Identity
    authentication
    Noisy None