Experimental Investigation of Criteria for Continuous Variable Entanglement

We generate a pair of entangled beams from the interference of two amplitude squeezed beams. The entanglement is quantified in terms of EPR paradox and inseparability criteria, with both results clearly beating the standard quantum limit. We experimentally analyze the effect of decoherence on each criterion and demonstrate qualitative differences. We also characterize the number of required and excess photons present in the entangled beams and provide contour plots of the efficacy of quantum information protocols in terms of these variables.

Figure 1

Experimental schematic. BS (PBS): $50/50$ (polarizing) beam splitter; $\lambda /2$: half-wave plate; $\varphi$ and $\theta$: phase shift.

Figure 2

Comparison of (a) EPR and (b) inseparability criteria with varied detection efficiency. The symbols +, △, and ○ label three separate experimental runs. For + a systematic error was introduced by the detection dark noise when optimizing the EPR criterion gain. The solid fit in (a) includes this; the dashed fit is the result expected if the error was eliminated and agrees well with runs △ and ○. The solid line in (b) is a theoretical fit; the dashed line is the result predicted by the fit in (a). There were four sources of unavoidable loss in our system: I, detection loss; II, homodyne loss; III, optical loss; IV, OPA escape loss.

Figure 3

Frequency spectra of (a) ${\Delta }^2{\widehat{X}}_{x\pm y}^{+}$ and (b) ${\Delta }^2{\widehat{X}}_{x\pm y}^{-}$ for our entangled beams with no additional loss.

Figure 4

Spectra of (a) $\sqrt{{\Delta }^2{X}_{x\pm y}^{+}{\Delta }^2{X}_{x\pm y}^{-}}$, and (b) the average of the quadrature noise variances of the individual entangled beams, with no additional loss.

Figure 5

Experimental results on photon number plots. The contours on the plots are (a) EPR criterion, (b) fidelity measure of teleportation, and (c),(d) ratio of dense-coding channel capacity to optimum squeezed channel capacity for mean photon numbers of 6.75 and 250, respectively.