Sharing a quantum secret without a trusted party

In a conventional quantum (k, n) threshold scheme, a trusted party shares a secret quantum state with n participants such that any k of those participants can cooperate to recover the original secret, while fewer than k participants obtain no information about the secret. In this paper we show how to construct a quantum (k, n) threshold scheme without the assistance of a trusted party, who generates and distributes shares among the participants. Instead, each participant chooses his private state and contributes the same to the determination of the final secret quantum state.