Secret Sharing with a Single d-level Quantum System

Secret sharing is a cryptographic primitive which plays a central role in various secure multiparty computation tasks and management of keys in cryptography. In secret sharing protocols, a message is divided into shares given to recipient parties in such a way that some number of parties need to collaborate in order to reconstruct the message. Quantum protocols for the task commonly rely on multipartite entanglement. We present a multiparty quantum secret sharing protocol which requires only sequential communication of a single d-level system (for any prime d). It is scalable and can be realized with the state of the art technology.