Measurement-device-independent quantum secret sharing and quantum conference based on Gaussian cluster state

Abstract

Cluster state is the basic resource for one-way quantum computation and a valuable resource for establishing quantum network, because it has a flexible and varied composition form. We present measurement-device-independent quantum secret sharing (QSS) and quantum conference (QC) schemes based on continuous variable (CV) four-mode cluster state with different structures. The users of the protocol prepare their own Einstein-Podolsky-Rosen (EPR) states, respectively. One mode of these EPR states is sent to an untrusted relay where a generalized Bell measurement creates different types of CV cluster states among four users, while the other mode is kept at their own station. We show that a shared secret key for QSS and QC schemes is distilled based on the shared quantum correlation among four users. QC and four users QSS are implemented based on the star shape CV cluster state. QSS with three users are implemented based on the linear or square shape CV cluster states. The results show that the secure transmission distance for an asymmetric network, where the transmission distances between the users and relay are different, is longer than that of a symmetric network, where the transmission distances between the users and relay are the same. The presented schemes provide concrete references for establishing quantum network with the CV cluster state.