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Communications in Theoretical Physics

Knotted Picture of Unknown Quantum State in Process of Quantum Teleportation

Gu Zhi-Yu, Qian Shang-Wu

Published May 1, 2008• 6 citations
Publisher

Abstract

This paper gives the knotted picture of the unknown quantum state in the process of quantum teleportation and the surgical knotted operations of the unitary operators operated on the teleported quantum state.
DOI
10.1088/0253-6102/49/5/16

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Quantum teleportation is a method to transfer unknown quantum states to a distant place with an assist of quantum entanglement. Whole process of the teleportation can be described by a transfer-operator. It allows us to calculate the output state in the case of the teleportation using non-maximal entanglement. This method investigates the properties of some of the output states. The photon statistics of the teleportation output are determined and the correlation between the field information β obtained in the teleportation process and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of a qubit encoded in the polarization of a single-photon state.
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.