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SCIENCE CHINA Information Sciences, Volume 62, Issue 7: 072501(2019) https://doi.org/10.1007/s11432-018-9705-x

Measurement-device-independent quantum secret sharing and quantum conference based on Gaussian cluster state

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  • ReceivedSep 3, 2018
  • AcceptedNov 21, 2018
  • PublishedMay 7, 2019

Abstract

Cluster state is the basic resource for one-way quantum computation and a valuable resource for establishing quantum network, because it has a flexible and varied composition form. We present measurement-device-independent quantum secret sharing (QSS) and quantum conference (QC) schemes based on continuous variable (CV) four-mode cluster state with different structures. The users of the protocol prepare their own Einstein-Podolsky-Rosen (EPR) states, respectively. One mode of these EPR states is sent to an untrusted relay where a generalized Bell measurement creates different types of CV cluster states among four users, while the other mode is kept at their own station. We show that a shared secret key for QSS and QC schemes is distilled based on the shared quantum correlation among four users. QC and four users QSS are implemented based on the star shape CV cluster state. QSS with three users are implemented based on the linear or square shape CV cluster states. The results show that the secure transmission distance for an asymmetric network, where the transmission distances between the users and relay are different, is longer than that of a symmetric network, where the transmission distances between the users and relay are the same. The presented schemes provide concrete references for establishing quantum network with the CV cluster state.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 11504024, 11834010, 61602045, 11522433, 61502041, 61602046), National Key Research and Development Program of China (Grant No. 2016YFA0302600, 2018YFA0306404, 2016YFA0301402), and Program of Youth Sanjin Scholar.


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  • Figure 1

    (Color online) The four-partite cluster states. Each cluster node, corresponding to an optical mode, is represented by a circle. Neighboring nodes are connected by lines. (a), (b) and (c) represent star, linear and square shape cluster state, respectively.

  • Figure 2

    (Color online) Basic protocol for MDI quantum network with a four-mode cluster state. Alice, Bob, Charlie and David prepare an EPR state, respectively. They hold one mode ($\hat{b}_{i},i\in \{1-4\}$) of the EPR state in their own station and send the other mode ($\hat{a}_{i},i\in~\{1-4\}$) to an untrusted relay. After receiving the modes from Alice, Bob, Charlie and David, the Bell measurement is performed in the relay. Displacement operations are performed on the modes ($\hat{b}_{i},i\in \{1-4\}$) after the users obtain the measurements results from the relay. HBS, half beam splitter.

  • Figure 3

    (Color online) Scheme against a coherent attack. Eve chooses four pure Gaussian states ($\hat{E}_{a_{i}},i=1-4$) from his ancillary qumodes (AQ), and injects them into the channel between Alice (Bob, Charlie, David) and the relay by beam splitter whose transmission efficiency is $\eta~_{i}$ ($i=1-4$). One of the output modes is sent to the relay as a fake mode, while the other modes and the remaining AQ are stored in Eve's quantum memory (QM).

  • Figure 10

    (Color online) The secret key rate versus variance of EPR states for four users QSS, three users QSS and QC protocols. Line (1) four users QSS; line (2) three users QSS; line (3) QC protocol.

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