We present three schemes for the joint remote state preparation (JRSP) of an arbitrary four-qubit W-type entangled state with complex coefficients via four and two three-qubit GHZ states as the quantum channel. In these schemes, two senders (or $N$ senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It isshown that, only if two senders (or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits, the receiver can reconstruct the original state by means of some appropriate unitary operations. It is shown that, in all our schemes, the total success probability of the JRSP can reach 1. Specially, compared with the first scheme in our paper, the entanglement resource in the second scheme can be reduced. This means that the scheme is more efficient and economical.

In this paper, we present a scheme which can produce a perfect copy of an unknown single-particle four-dimensional quantum state with assistance from a state preparer. Two stages were included in this scheme. The first stage requires the usual teleportation, after Alice’s (the state sender) generalised Bell state measurement. Bob (the state receiver) can get the original state with unit probability. In the second stage, after having received Victor’s (the state preparer) classical message, and using the rest resource of the teleportation process, the perfect copy of an original unknown state can be produced in Alice’s place. To realise the scheme, several novel sets of measuring basis were introduced. It must be pointed out that, in the present scheme, the total success probability for assisted cloning of a perfect copy of the unknown state can reach 1.