Quantum versus classical domains for teleportation with continuous variables

By considering the utilization of a classical channel without quantum entanglement, fidelity F₂₋₀ₒₒ₈₂₀₋=12 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, 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 F₂₋₀ₒₒ₈₂₀₋=12. Likewise, violations of local realism onset at this same threshold, with the added requirement of overall efficiency >23 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.