The Unitary Transformation in Quantum Teleportation

In the well known treatment of quantum teleportation, the receiver should convert the state of his EPR particle into the replica of the unknown quantum state by one of four possible unitary transformations. However, the importance of these unitary transformations must be emphasized. We will show in this paper that the receiver can not transform the state of his particle into an exact replica of the unknown state which the sender want to transfer if he have not a proper implementation of these unitary transformations. In the procedure of converting state, the inevitable coupling between EPR particle and environment which is needed by the implementation of unitary transformations will reduce the accuracy of the replica. 03.67.Hk, 03.67.-a, 03.65.Ta.. In 1993, Bennett et al.[1] proposed a famous treatment to transfer an intact quantum state from one place to another by use of the long-range correlation between EPR pair of particles. In their scheme, an unknown state and one of EPR particles are given to the sender, and the sender then perform a complete measurement on the joint system of the unknown state and her EPR state. After this, the receiver will perform a unitary transformation on the second particle of the EPR pair to obtain the replica of the unknown state, certainly, this unitary transformation is determined by the results of measurement told by the sender through a classical channel. The experimental realizations of their treatment were exhibited by Bouwmeester et al.[2] and Boschi et al.[3], respectively, in which an initial photon which carries the polarization is transferred by use of a pair of entangled photons prepared in an EPR state. These approaches to quantum teleportation had inspired many investigations into this field, such as the discussions of continuous variable quantum teleportation[4, 5, 6], the analysis of quantum fluctuation in the teleportation[7] etc. However, it should be pointed out that the physical implementation of the unitary transformations on the second EPR particle should be noticed, they