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International Journal of Quantum Information

CONTINUOUS VARIABLE TELEPORTATION OF QUANTUM FIELDS

H. J. Carmichael

Published Nov 1, 2005• 5 citations
Publisher

Abstract

A quantum trajectory formulation of broadband continuous variable teleportation is developed. Inputs and outputs are quasi-monochromatic quantum fields rather than single-mode quantum states. The formalism accounts for the continuous measurements of Alice and Victor and continuous displacement of the teleported field by Bob. It is applied to the teleportation of the Mollow spectrum and photon antibunching in single-atom resonance fluorescence.

DOI
10.1142/s0219749905001213

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Foundations of Quantum Mechanics in the Light of New Technology•Oct 1, 2002•1 citation
A quantum trajectory formulation of broadband continuous variable teleportation is developed. Inputs and outputs are quasi-monochromatic quantum fields rather than single-mode quantum states. The formalism accounts for the continuous measurements of Alice and Victor and continuous displacement of the teleported field by Bob. It is applied to the teleportation of the Mollow spectrum and photon antibunching in single-atom resonance fluorescence.
Quantum trajectory equations are formulated for continuous variable teleportation, which model the generation of finite bandwidth squeezed light, the homodyne measurements carried out by Alice, and take into account the continuous feed-forward of Alice's measurement results to Bob. The formulation is multi-mode and provides direct access to correlation functions of the output field detected by Victor. Three unravellings of the dynamics are considered, corresponding to Victor's choice of direct, homodyne, or heterodyne detection of the output field. Numerical results for the teleportation of a vacuum-state input field are presented.
Quantum teleportation of an unknown broadband electromagnetic field is investigated. The continuous-variable teleportation protocol by Braunstein and Kimble [Phys. Rev. Lett. 80, 869 (1998)] for teleporting the quantum state of a single mode of the electromagnetic field is generalized for the case of a multimode field with finite bandwith. We discuss criteria for continuous-variable teleportation with various sets of input states and apply them to the teleportation of broadband fields. We first consider as a set of input fields (from which an independent state preparer draws the inputs to be teleported) arbitrary pure Gaussian states with unknown coherent amplitude (squeezed or coherent states). This set of input states, further restricted to an alphabet of coherent states, was used in the experiment by Furusawa et al. [Science 282, 706 (1998)]. It requires unit-gain teleportation for optimizing the teleportation fidelity. In our broadband scheme, the excess noise added through unit-gain teleportation due to the finite degree of the squeezed-state entanglement is just twice the (entanglement) source's squeezing spectrum for its ``quiet quadrature.'' The teleportation of one half of an entangled state (two-mode squeezed vacuum state), i.e., ``entanglement swapping,'' and its verification are optimized under a certain nonunit gain condition. We will also give a broadband description of this continuous-variable entanglement swapping based on the single-mode scheme by van Loock and Braunstein [Phys. Rev. A 61, 10 302 (2000)].
The ultimate limits of continuous-variable single-mode quantum teleportation due to absorption are studied, with special emphasis on (quasi-) monochromatic optical fields propagating through fibers. It is shown that even if an infinitely squeezed two-mode squeezed vacuum were used, the amount of information that would be transferred quantum mechanically over a finite distance is limited and effectively approaches zero on a length scale that is much shorter than the (classical) absorption length. The state-dependent teleportation fidelity can be close to unity only for short distances. To realize the largest possibly fidelity, asymmetrical equipment must be used, where the source of the two-mode squeezed vacuum is nearer to Alice than to Bob and as a consequence the coherent displacement performed by Bob cannot be chosen independently of the transmission lengths.
We develop a simple and efficient theoretical model to understand the quantum properties of broadband continuous variable quantum teleportation. We show that, if stated properly, the problem of multimode teleportation can be simplified to teleportation of a single effective mode that describes the input state temporal characteristic. Using that model, we show how the finite bandwidth of squeezing and external noise in the classical channel affect the output teleported quantum field. We choose an approach that is especially relevant for the case of non-Gaussian nonclassical quantum states and we finally back-test our model with recent experimental results.
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