How to Share a Quantum Secret

We investigate the concept of quantum secret sharing. In a $(k,n)$ threshold scheme, a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret, but any set of k-1 or fewer shares contains absolutely no information about the secret. We show that the only constraint on the existence of threshold schemes comes from the quantum ``no-cloning theorem,'' which requires that $n<2k$, and we give efficient constructions of all threshold schemes. We also show that, for k≤n<2k-1, then any $(k,n)$ threshold scheme must distribute information that is globally in a mixed state.