Verifiable (t,n) threshold quantum secret sharing using d-dimensional Bell state

• We use the d-dimensional Bell state and Lagrange interpolation to propose a verifiable (t, n) threshold QSS scheme.
• The participants perform the unitary operations on the d-dimensional Bell state to reconstruct the secret.
• The recovered secret can be verified to check whether some dishonest participants provide fake shadows.
• The proposed scheme needs less verification information and can give more perfect security proof.

A verifiable (t,n)(t,n) threshold quantum secret sharing scheme is proposed by using the d-dimensional Bell state and the Lagrange interpolation. In the proposed scheme, the dealer distributes the shadows to the participants through the quantum direct communication. In the recovery phase, the dealer generates a two-qudit Bell state in the d-dimensional Hilbert space, and the participants perform the unitary operations on the Bell state to reconstruct the secret. The participants can judge whether the recovered secret is the original one, and check whether some dishonest participants provide the fake shadows in the reconstruction. Compared to the existing verifiable quantum secret sharing schemes, the proposed scheme needs less verification information, and can give more perfect security proof.