Bidirectional controlled quantum state preparation in high-dimensional quantum system

High-dimensional quantum system exhibits unique advantages over the qubit system in some quantum information processing tasks. We present a program for implementing deterministic bidirectional controlled remote quantum state preparation (BCRSP) in arbitrary $N$-dimensional (quNit) system. By introducing two generalized Greenberger-Horne-Zeilinger (GHZ) states as quantum channels, two communication parties can simultaneously prepare a single-particle high-dimensional state at each other's site under the control of Charlie. Compared with the previous counterparts, the significant advantage of our scheme is that the high-dimensional CNOT operations are not required. Moreover, the performance our scheme are evaluated. The evaluation of the performance shows that if the quNit is encoded in the spatial mode of single photons, our scheme can be accomplished solely using only linear optical elements.