Bidirectional controlled remote state preparation in four-dimensional systems

In this paper, two novel schemes for bidirectional controlled remote state preparation (BCRSP) and asymmetric bidirectional controlled remote state preparation (ABCRSP) in four-dimensional systems are proposed. The first scheme uses a six-particle entangled state as the quantum channel. Under Charlie’s supervision, Alice and Bob can simultaneously create a single-particle four-dimensional equatorial state at each other’s location. Moreover, in the second scheme, using a seven-particle entangled state as the quantum channel, Alice remotely prepares a two-particle four-dimensional equatorial state for Bob, while Bob remotely prepares another single-particle four-dimensional equatorial state for Alice under the supervision of controller Charlie. Both schemes employ quantum operations such as control-not, projective measurement and unitary transformation in four-dimensional systems. It is worth noting that the proposed schemes have a total success probability of 100% in ideal environment. In addition, we also investigate the proposed two schemes in the noisy environment. The fidelities of output states are calculated and the effect factors are discussed. Finally, we give the advantages of these schemes compared to other schemes.