Resources required for exact remote state preparation

It has been shown [M.-Y. Ye, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A. 69, 022310 (2004)] that it is possible to perform exactly faithful remote state preparation using finite classical communication and any entangled state with maximal Schmidt number. Here we give an explicit procedure for performing this remote state preparation. We show that the classical communication required for this scheme is close to optimal for remote state preparation schemes of this type. In addition we prove that it is necessary that the resource state have maximal Schmidt number.

Figure 1

The entanglement versus classical communication for the exact RSP of qubit states using a partially entangled state. The solid curve is that based on the first scheme given, and the dotted line gives the communication required when ${\beta }_0$ is taken to be real. The dashed-dotted line is the upper bound on the communication for the nonconstructive scheme, and the dashed line is a lower bound on the communication.