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Criteria for Continuous-Variable Quantum Teleportation

Braunstein, S L, Christopher A. Fuchs, Kimble, H J

Published Oct 8, 1999• 114 citations
OpenAlex

Abstract

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 $0.58 \\pm 0.02$ 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.

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arXiv:quant-ph/0207076•Physical Review A•Mar 11, 2003•254 citations
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.
By considering the utilization of a classical channel without quantum entanglement, fidelity Fclassical=12{F}_{\mathrm{classical}}=\frac{1}{2}Fclassical​=21​ has been established as setting the boundary between classical and quantum domains in the teleportation of coherent states of the electromagnetic field [S. L. Braunstein, C. A. Fuchs, and H. J. Kimble, J. Mod. Opt. 47,47,47, 267 (2000)]. We further examine the quantum-classical boundary by investigating questions of entanglement and Bell-inequality violations for the Einstein-Podolsky-Rosen states relevant to continuous variable teleportation. The threshold fidelity for employing entanglement as a quantum resource in teleportation of coherent states is again found to be Fclassical=12.{F}_{\mathrm{classical}}=\frac{1}{2}.Fclassical​=21​. Likewise, violations of local realism onset at this same threshold, with the added requirement of overall efficiency $\ensuremath{\eta}>\frac{2}{3}$ in the unconditional case. By contrast, recently proposed criteria adapted from the literature on quantum-nondemolition detection are shown to be largely unrelated to the questions of entanglement and Bell-inequality violations.
We experimentally demonstrate quantum teleportation for continuous variables using squeezed-state entanglement. The teleportation fidelity for a real experimental system is calculated explicitly, including relevant imperfection factors such as propagation losses, detection inefficiencies, and phase fluctuations. The inferred fidelity for input coherent states is $F=0.61\ifmmode\pm\else\textpm\fi{}0.02,$ which when corrected for the efficiency of detection by the output observer, gives a fidelity of 0.62.0.62.0.62. By contrast, the projected result based on the independently measured entanglement and efficiencies is 0.69.0.69.0.69. The teleportation protocol is explained in detail, including a discussion on discrepancy between experiment and theory, as well as on the limitations of the current apparatus.