Probabilistic joint remote preparation of a two-particle high-dimensional equatorial state

In this work, using two-particle high-dimensional orthogonal projective measurement and some appropriate unitary operations we realize the joint remote preparation of an arbitrary two-particle high-dimensional equatorial state. The total success probability is found to only depend on the coefficients of the entangled states shared between the two preparers and the receiver, and the classical communication cost is also calculated. The three-party high-dimensional case is extended to multi-party high-dimensional as well.