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arXiv:quant-ph/9903003 · Journal of Optics B Quantum and Semiclassical Optics

Characterizing teleportation in optics

Timothy C. Ralph, Ping Koy Lam, Rodney Polkinghorne

Published Aug 1, 1999• 33 citations
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Abstract

We discuss the characterization of continuous variable, optical quantum teleportation in terms of the two-quadrature signal transfer and conditional variances between the input and output states. We derive criteria which clearly define the classical limits and highlight interesting operating points which are not obvious from a calculation of the fidelity of the teleportation alone.

DOI
10.1088/1464-4266/1/4/321

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We discuss the characterization of continuous variable, optical quantum teleportation in terms of the two-quadrature signal transfer and conditional variances between the input and output states. We derive criteria which clearly define the classical limits and highlight interesting operating points which are not obvious from a calculation of the fidelity of the teleportation alone.
We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of 0.58pm0.020.58 \\pm 0.020.58pm0.02 was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.
We report the experimental demonstration of quantum teleportation of the quadrature amplitudes of a light field. Our experiment was stably locked for long periods, and was analyzed in terms of fidelity F\mathcal{F}F and with signal transfer ${T}_{q}{=T}^{+}{+T}^{\ensuremath{-}}$ and noise correlation ${V}_{q}{=V}_{\mathrm{in}\mathrm{|}\mathrm{}\mathrm{out}}^{+}{V}_{\mathrm{in}\mathrm{|}\mathrm{}\mathrm{out}}^{\ensuremath{-}}.$ We observed an optimum fidelity of $0.64\ifmmode\pm\else\textpm\fi{}0.02,$ ${T}_{q}=1.06\ifmmode\pm\else\textpm\fi{}0.02,$ and ${V}_{q}=0.96\ifmmode\pm\else\textpm\fi{}0.10.$ We discuss the significance of both Tq>1{T}_{q}>1Tq​>1 and Vq<1{V}_{q}<1Vq​<1 and their relation to the teleportation no-cloning limit.
We investigate continuous variable quantum teleportation. We discuss the methods presently used to characterize teleportation in this regime, and propose an extension of the measures proposed by Grangier and Grosshans , and Ralph and Lam . This new measure, the gain normalized conditional variance product M, turns out to be highly significant for continuous variable entanglement swapping procedures, which we examine using a necessary and sufficient criterion for entanglement. We elaborate on our recent experimental continuous variable quantum teleportation results , demonstrating success over a wide range of teleportation gains. We analyze our results using fidelity; signal transfer, and the conditional variance product; and a measure derived in this paper, the gain normalized conditional variance product.