How to share a quantum secret

We investigate the concept of quantum secret sharing. In a (k, ta) 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 less than or equal to n < 2k - 1, then any (k, n) threshold scheme must distribute information that is globally in a mixed state.