Classification of Small-size Quantum Secret Sharing Schemes using Uniform States

Abstract:We study the connection between quantum secret sharing (QSS) schemes and $k$-uniform states of qubits beyond the equivalence between threshold QSS schemes and AME states. Specifically, we show that $3$-uniformity is a necessary but not sufficient condition for constructing a $3$-homogeneous QSS scheme using states of qubits. To the best of our knowledge, this is the first result connecting \emph{non-threshold} QSS schemes with $k$-uniform states. As an application of our result, we classify QSS schemes for up to 7 players and provide explicit characterizations of their existence. Our results offer new insights into the role of $k$-uniform states in the design of QSS schemes (not necessarily threshold) and provide a foundation for future classifications of QSS schemes with more complex structures.

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2510.07753 [quant-ph]

(or arXiv:2510.07753v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2510.07753 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.