In $(\kappa,\eta)$ threshold secret sharing schemes, a secret is divided into$\eta$ shares, and any group of fewer than $\kappa$ players have no informationabout the secret. We here present an $(N-1,N-1)$ threshold quantum secretsharing protocol on a given $N$-qubit state close to theGreenberger-Horne-Zeilinger state. In our protocol, $N$ players use aninequality derived from the Mermin inequality to check secure correlation ofclassical key bits for secret sharing. We show that if our inequality holdsthen every legitimate player can have key bits with positive key rate.Therefore, for sufficiently many copies of the state, the players can securelyshare a classical secret with high probability by means of our protocol.
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机译：在$（\ kappa，\ eta）$阈值秘密共享方案中，秘密被分成$ \ eta $份额，并且少于$ \ kappa $的玩家的任何组都没有有关秘密的信息。我们在这里给出了在接近Greenberger-Horne-Zeilinger状态的给定$ N $-量子位状态下的$（N-1，N-1）$门限量子秘密共享协议。在我们的协议中，$ N $玩家使用源自Mermin不等式的不等式来检查经典密钥位的安全相关性以进行秘密共享。我们证明，如果我们的不等式成立，那么每个合法玩家都可以拥有正密钥率的密钥位，因此，对于足够多的状态副本，玩家可以通过我们的协议安全地共享经典机密。
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