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

TL;DR

This paper introduces new procedures for ramp quantum secret sharing schemes that allow some shares to be distributed before the secret is known, maintaining high coding rates and broadening practical applicability.

Contribution

It proposes novel encoding procedures for ramp quantum secret sharing schemes that enable pre-distribution of shares without compromising their coding rate.

Findings

Procedures enable pre-distribution of shares in ramp schemes.

High coding rates are preserved with new procedures.

Applicability to scenarios with unavailable participants is improved.

Abstract

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.