Advance Sharing Procedures for the Ramp Quantum Secret Sharing Schemes With the Highest Coding Rate

In some quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. However, it is unclear whether some shares can be distributed before a secret is given in the ramp quantum secret sharing schemes with the highest coding rate. In this paper, we propose methods to distribute some shares before a secret is given in those schemes, then we prove that our new encoding procedures retain the correspondences between quantum secrets and quantum shares in the original schemes.