Advance sharing for stabilizer-based quantum secret sharing schemes

TL;DR

This paper investigates the conditions under which shares in stabilizer-based quantum secret sharing can be distributed in advance, providing new insights and a scheme where all forbidden sets are eligible for early sharing.

Contribution

It demonstrates that not all forbidden sets are advance shareable and introduces a new quantum secret sharing scheme where every forbidden set can be shared in advance.

Findings

Identified a forbidden set that is not advance shareable in existing schemes.

Proposed a new scheme where all forbidden sets are advance shareable.

Abstract

In stabilizer-based quantum secret sharing schemes, it is known that some shares can be distributed to participants before a secret is given to the dealer. This distribution is known as advance sharing. It is already known that a set of shares is advance shareable only if it is a forbidden set. However, it was not known whether any forbidden set is advance shareable. We provide an example of a set of shares such that it is a forbidden set but is not advance shareable in the previous scheme. Furthermore, we propose a quantum secret sharing scheme for quantum secrets such that any forbidden set is advance shareable.