关键词: 门限量子秘密共享, [d]维多粒子纠缠态, 纠缠交换, 联合投影测量

Abstract: In order to overcome the limitation on 2-dimension of Hilbert space, and solve the problem that some participants cannot attend reconstructing process of the shared secret, a （t, n） threshold quantum secret sharing scheme is proposed by using maximally d-dimensional multi-particle entanglement state. The dealer prepares n d-dimensional 2-particle entangled pairs and distributes the 2nd particle to n participants respectively. When the dealer chooses t particles in his hand for joint projection measurement, the entanglement swapping causes the corresponding t particles in participants’ hands to collapse into a t-particle entangled state. These t participants add their share to the t-particle entangled state through QFT transformation and Pauli operation. Eventually, the shared secret is recovered by these t participants. Security analysis shows that the proposed scheme can resist intercept-resend attack, entangle-measure attack, collusion attack, and forgery attack.

Key words: threshold quantum secret sharing, d-dimensional multi-particle entanglement state, entanglement swapping, joint projection measurement