Advance Sharing with Ogawa et al.'s Ramp Quantum Secret Sharing Scheme

TL;DR

This paper explores the possibility of distributing shares before the secret in Ogawa et al.'s ramp quantum secret sharing scheme, providing conditions for such pre-distribution while maintaining the scheme's properties.

Contribution

It introduces a method for pre-distributing shares in Ogawa et al.'s scheme and establishes necessary and sufficient conditions for such pre-distribution.

Findings

Pre-distribution of shares is possible under certain conditions.

A necessary and sufficient condition for pre-distribution is derived.

The scheme's coding rate remains optimal with the proposed method.

Abstract

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.