Joint remote preparation of four-qubit cluster-type states

We propose several schemes for the joint remote preparation of four-qubit cluster-type states with real coefficients and complex coefficients by using six Einstein-Podolsky-Rosen (EPR) pairs and two six-qubit entangled states as quantum channels respectively. In these schemes, two senders share the original state which they wish to help the receiver to remotely prepare. It is shown that, only if two senders collaborate with each other, and perform four-qubit projective measurements on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations.