Probabilistic joint remote preparation of a high-dimensional equatorial quantum state

This paper proposes a scheme for probabilistic joint remote preparation of an arbitrary high-dimensional equatorial quantum state by using high-dimensional single-particle orthogonal projective measurement and appropriate unitary operation. As a special case, a scheme of joint remote preparation of a single-qutrit equatorial state is presented in detail. The scheme is also generalized to the multi-party high-dimensional case. It shows that, only if when all the senders collaborate with each other, the receiver can reconstruct the original state with a certain probability.