Theory of quantum secret sharing

TLDR

The paper presents results on quantum secret sharing theory and discusses classical secret sharing using quantum states. The study shows that mixed‑state quantum secret sharing schemes arise by discarding a share from a pure‑state scheme, that each share must be at least as large as the secret, that general access structures are constrained only by monotonicity and the no‑cloning theorem, and that classical secrets can sometimes be shared with shares half the secret size.

Abstract

I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum secret sharing scheme must be at least as large as the size of the secret. I show that the only constraints on the existence of quantum secret sharing schemes with general access structures are monotonicity (if a set is authorized, so are larger sets) and the no-cloning theorem. I also discuss some aspects of sharing classical secrets using quantum states. In this situation, the size of each share can sometimes be half the size of the classical secret.