SCIENCE CHINA Information Sciences, Volume 61 , Issue 2 : 022501(2018) https://doi.org/10.1007/s11432-016-9151-x

A secure rational quantum state sharing protocol

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  • ReceivedDec 11, 2016
  • AcceptedJan 16, 2017
  • PublishedSep 28, 2017



This work was supported by National Natural Science Foundation of China (Grant Nos. 61671087, 61272514, 61170272), National Development Foundation for Cryptological Research (Grant No. MMJJ201401012), Fok Ying Tung Education Foundation (Grant No. 131067), Natural Science Foundation of Inner Mongolia (Grant No. 2017MS0602), University Scientific Research Project of Inner Mongolia (Grant No. NJZY17164), and Open Foundation of Guizhou Provincial Key Laboratory of Public Big Data (Grant No. 2017BDKFJJ007).


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  • Table 1   The detailed strategies, outcomes, and utilities
    The value of ${\rm~list}_i$ Role Strategy Outcome Explanation Utility
    0 Any agent $Cooperating$ $Passed$ The agent passes the check. $U_g$
    0 Any agent $Cheating$ $Failed$ The agent does not pass the check. $U_f$
    1 Bob$_k$ $Recovering$ $True~state$ The agent Bob$_k$ obtains the true state successfully. $U_s$
    1 Bob$_k$ $Recovering$ $False~state$ The agent Bob$_k$ obtains a false state. $U_e$
    1 Bob$_i$ ($i$$\ne$$k$) $Cheating$ $Threatening$ The agent Bob$_i$ ($i$$\ne~$$k$) threatens that his results are wrong. $U_t$
    1 Bob$_i$ ($i$$\ne$$k$) $Cooperating$ $Successfully$ $helping$ The agent Bob$_i$ ($i$$\ne$$k$) helps Bob$_k$ obtain the state successfully. $U_{ps}$
    1 Bob$_i$ ($i$$\ne$$k$) $Cooperating$ $Unsuccessfully$ $helping$ The agent Bob$_i$ ($i$$\ne$$k$) wants to help Bob$_k$, but Bob gets a false state since some-one else is threatening. $U_{pe}$
  • Table 2   The strategies and utilities in a two-agent version
    $Cheating$ $Cooperating$
    $Cheating$ ($U_A$, $U_A$) ($U_B$, $U_C$)
    $Cooperating$ ($U_C$, $U_B$) ($U_D$, $U_D$)

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