How to share a quantum secret

Abstract

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. © 1999 The American Physical Society.