Quantum versus Classical Domains for Teleportation with Continuous Variables

By considering the utilization of a classical channel without quantum entanglement, fidelity F sub classical = 1/2 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 EPR states relevant to continuous variable teleportation. The threshold fidelity for employing entanglement as a quantum resource in teleportion of coherent states is again found to be F sub classical = 1/2. Likewise, violations of local realism onset at this same threshold, with the added requirement of overall efficiency eta > 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.