Advance Sharing With Ogawa Et Al.S Ramp Quantum Secret Sharing Scheme for Prime-Dimensional Quantum Systems

The ramp quantum secret sharing proposed by Ogawa et al. has the highest possible coding rate given a threshold type access structure. On the other hand, 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 Ogawa et al.'s scheme. In this paper, we propose a method to distribute some shares before a secret is given in Ogawa et al.'s scheme, then determine a necessary and sufficient condition on sets of shares that can be distributed before a given secret.