Bidirectional controlled remote state preparation in three-dimensional system

We present a novel scheme for bidirectional controlled remote state preparation (BCRSP) in a three-dimensional system with a six-qutrit entangled state as the quantum channel. In this scheme, two distant parties, Alice and Bob, are not only senders but also receivers. Alice wants to remotely prepare a single-qutrit equatorial state at Bob's site, while at the same time, Bob wishes to help Alice by remotely preparing another single-qutrit equatorial state. It is shown that, only if the two senders and the controller collaborate with each other, the BCRSP can be completed successfully.