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 procedures to distribute some shares before a secret is given in those schemes. The new procedures enhances applicability of the secret sharing schemes to wider scenarios as some participants can be unavailable when the dealer obtains the quantum secret. Then we prove that our new encoding procedures retain the correspondences between quantum secrets and quantum shares in the original schemes, which ensures the highest coding rates of the original schemes are also retained.
ieeeaccess.cls, 7 pages, no figure. Version 2 is the accepted-version by IEEE Transactions on Quantum Engineering. This is a full journal paper version of the previous conference paper arXiv:2404.15646. The difference to arXiv:2404.15646 is clearly indicated in the introduction