Advance sharing for stabilizer-based quantum secret sharing schemes
Mamoru Shibata
TL;DR
The paper investigates advance sharing in stabilizer-based quantum secret sharing (QSS) and the relationship between forbidden sets and advance shareable sets. It first provides a counterexample showing that not all forbidden sets are advance shareable under the prior EAQECC-based scheme. It then proposes a unitary-transformation-based advance sharing construction for stabilizer-based QSS, proving that a set is advance shareable if and only if it is forbidden, thereby maximizing the advance shareable portion of the access structure. The work clarifies how pre-distribution of shares can be integrated with access structures in quantum networks and resolves discrepancies between forbidden sets and advance shareability observed in previous schemes.
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.