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Physical Review A

Complete teleportation of a paraxial single-photon field

Diney S. Ether, Stephen Patrick Walborn, Nicim Zagury

Published Mar 6, 2009• 4 citations
Publisher

Abstract

We discuss the complete teleportation of the unknown quantum state of a paraxial single-photon field. The term complete signifies that the teleportation procedure transmits the entire quantum state, which is codified in all the degrees of freedom of a paraxial single-photon field: the polarization, the transverse wave vector, and the frequency. We analyze several illustrative examples and propose a possible experimental scheme.

DOI
10.1103/physreva.79.032305

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We discuss the complete teleportation of the unknown quantum state of a paraxial single-photon field. The term complete signifies that the teleportation procedure transmits the entire quantum state, which is codified in all the degrees of freedom of a paraxial single-photon field: the polarization, the transverse wave vector, and the frequency. We analyze several illustrative examples and propose a possible experimental scheme.
Recent demonstrations of teleportation have transferred quantum information encoded into either polarization or field-quadrature degrees of freedom (DOFs), but an outstanding question is how to simultaneously teleport quantum information encoded into multiple DOFs. We describe how the transverse-spatial, spectral and polarization states of a single photon can be simultaneously teleported using a pair of multimode, polarization-entangled photons derived from spontaneous parametric down-conversion. Furthermore, when the initial photon pair is maximally entangled in the spatial, spectral, and polarization DOFs then the photon’s full quantum state can be reliably teleported using a Bell-state measurement based on sum-frequency generation.
We report how quantum information encoded into multiple photonic degrees of freedom may be simultaneously teleported using a single, common physical process. The application of teleportation to the complete quantum state of a photon, i.e. the spectral, spatial, and polarization component states, permits the full photonic Hilbert space to be used for encoding information while simultaneously enabling subspaces to be addressed individually, e.g. for quantum information processing. We analyze the feasibility of teleporting the full quantum state through numerical analysis of the fidelity under nominal experimental conditions and for different types of input states, e.g. single-photon states that are separable or entangled in the physical degrees of freedom.
By using the quantum teleportation protocol, Alice can send an unknown quantum state (e.g. the polarization of a single photon) to Bob without ever knowing about it. This paper discusses a quantum teleportation experiment in which nonlinear interactions are used for the Bell state measurement. Since the Bell state measurement is based on nonlinear interactions, all four Bell states can be distinguished. Therefore, teleportation of a polarization state can occur with certainty, in principle. Details of the theory and the experimental set-up are discussed.
The teleportation of an unknown polarization state of one of the photons in a system of identical particles has been considered. It has been shown that the spatial degrees of freedom, which are various directions of the momentum of three photons, are of significant importance for teleportation in the system of identical particles. The inclusion of the spatial degrees of freedom increases the dimension of the space of single-particle states. In view of this increase, a four-dimensional subspace of two-particle states, which is similar to the space of states spanned on the Bell states in the system of two distinguishable qubits, can be separated in the experimental configuration.
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.