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arXiv:quant-ph/0604195 · Communications in Theoretical Physics

Unitary Transformation in Quantum Teleportation

Wang Zheng-Chuan

Published Nov 1, 2006• 0 citations
arXivHTMLPDF

Abstract

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 cannot transform the state of his particle into an exact replica of the unknown state which the sender wants to transfer if he has 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.

DOI
10.1088/0253-6102/46/5/018

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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 cannot transform the state of his particle into an exact replica of the unknown state which the sender wants to transfer if he has 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.
Teleporting a quantum state,the sender Alice disassembles the entire informations into two parts: one purely classical information and the another purely non-classical information,then sends them to the receiver Bob via two different channels.Firstly,sending the purely non-classical part,the EPR pair which consists of two fermions with the spin of 1 2 here plays the key role in the teleportation,one EPR particle is given to Alice,while the other is given to Bob.Alice performs a complete measurement of the von Neumann type on the joint system consisting of the original particle and her EPR particle,this measurement performed in the four eigenstates of the Bell operator leads to collapse the wave packet of the joint wavefunction into the four correlated Bell bases.Through applying the appropriate unitary transformation to the state of his EPR particle Bob can reconstruct a replica of the original state destroyed in Alice's hand.Moreover,this Bell measurement produces two bits of classical information which is sent to Bob,a quantum teleportation is therefore completed.The paper studies the interior relation between EPR pairs of particles and the quantum teleportation.
A scheme for teleportation of n-particle arbitrary states via n pairs of EPR states is proposed.In the scheme,we discovered the internal relationship between the result of Alice's measurement and the unitary transformation performed by Bob(the receiver),and the corresponding expressions were described.Thus when Bob receiving the result of Alice' Bell measurement,he can ascertain immediately the corresponding unitary transformation he must performed in order to implement the teleportation protocol,which is particularly important for the case that n is very large.
In this letter, a scheme of teleporting a N-particle entangled state is proposed. n EPR states are used as quantum channels, the sender wants to teleport a quantum state to the receiver, She makes n Bell-state measurement on particles belong to her, and sends the results of measurement through a classical information channel to the receiver, According to the measurement results of the sender, the receiver performs a respective unitary operator on particles belong to him. The teleportation is successfully realized, and the probability of successful telepotation is one. It is different from the scheme in ref. [7], the quantum logic circuit may be presented easily.