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Progress of Theoretical Physics Supplement

Quantum Teleportation Using a Transfer-Operator Method

Toshiki Ide

Published Jan 1, 2006• 1 citation
Publisher

Abstract

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.

DOI
10.1143/ptps.164.176

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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.
The properties of continuous-variable teleportation of single-photon states are investigated. The output state is different from the input state due to the nonmaximal entanglement in the Einstein–Podolsky–Rosen beams. The photon statistics of the teleportation output are determined, the correlation between the field information is 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
The properties of continuous-variable teleportation of single-photon states are investigated. The output state is different from the input state due to the nonmaximal entanglement in the Einstein-Podolsky-Rosen beams. The photon statistics of the teleportation output are determined and the correlation between the field information \ensuremath{\beta} 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.
The properties of continuous variable teleportation of single photon states are investigated. The output state is different from the input state due to the non-maximal entanglement in the EPR beams. 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 qbit encoded in the polarization of a single photon. 1
Quantum teleportation is the disembodied transport of an unknown quantum state |ψ〉 from one place to another. All protocols for accomplishing such transport require nonlocal correlations, or entanglement, between systems shared by sender and receiver. The sender is normally called Alice and the receiver is called Bob . Most attention has focused on teleporting the states of finite-dimensional systems, such as the two-dimensional polarization of a photon or the discrete level structure of an atom. First proposed in 1993 by Charles Bennett and his colleagues [17, 24, 138] quantum teleporation thus allows physicists to take a photon or any other quantum scale particle such as an atom and transfer its properties (such as the polarization) to another photon even if the two photons are on opposite sides of the galaxy. This scheme transports the particle’s properties to the remote location and not the particle itself. The state of the original particle must be destroyed to create an exact reconstruction at the other end. This is a consequence of the no cloning theorem. A role in the teleportation scheme is played by an entangled ancillary pair of particles which will be initially shared by Alice and Bob.
Quantum teleportation is possible because entanglement allows a definition of precise correlations between the noncommuting properties of a local system and corresponding noncommuting properties of a remote system. In this paper, the exact causality achieved by maximal entanglement is analyzed and the results are applied to the transfer of effects acting on the entanglement distribution channels to the teleported output state. In particular, it is shown how measurements performed on the entangled system distributed to the sender provide information on the teleported state while transferring the corresponding backaction to the teleported quantum state.
Superpositions of two orthogonal single-photon polarization states are commonly used as optical qubits. If such qubits are sent by continuous variable quantum teleportation, the modifications of the qubit states due to imperfect entanglement cause an increase in the average photon number of the output state. This effect can be interpreted as an accidental quantum cloning of the single photon input. We analyze the output statistics of the single photon teleportation and derive the transfer and cloning fidelities from the equations of the polarization qubit.