Last year two very similar proposals were put forward for "loophole-free" Bell tests:(adsbygoogle = window.adsbygoogle || []).push({});

R. García-Patrón Sánchez, J. Fiurácek , N. J. Cerf , J. Wenger , R. Tualle-Brouri , and Ph. Grangier, “Proposal for a Loophole-Free Bell Test Using Homodyne Detection”, Phys. Rev. Lett. 93, 130409 (2004)

http://arxiv.org/abs/quant-ph/0403191

and

Hyunchul Nha and H. J. Carmichael, “Proposed Test of Quantum Nonlocality for Continuous Variables”, PRL 93, 020401 (2004), http://arxiv.org/abs/quant-ph/0406101

Does anyone know if either has yet been done, and if not why not?

These really do seem likely not to have any loopholes, and hence, as a convinced local realist, I am confident that the Bell inequalities used will not be violated.

They present an opportunity for showing a much more striking difference between the QM and local realist models than most other Bell tests. The QM argument relies on theory that says that when you subtract a "photon" from a beam you can create a "non-classical" beam. Additional theory says that when you use such a beam as one input of a homodyne detector and take the average over all possible phase differences, the distribution of voltage differences that you obtain has a dip around zero that can be used as an indicator of the above non-classicality. It leads to negative values of the Wigner density.

Following from this nonclassical nature of the beam, the QM argument is that this will lead to the usual prediction for coincidence curves, vis a cos^2 curve that violates Bell inequalities.

But the classical approach for the same setup comes to a totally different conclusion. It agrees that the subtraction of the "photon" has a significant effect on the results, but this is only because, by measuring this photon and restricting attention to cases in which it is recorded in coincidence with its twin, you are selecting the most interesting signals, the ones with the neatest phase relationships and strongest correlations between the two PDC outputs.

It is phase relationship, not Wigner density, that is the important variable, and the dip around zero is a natural consequence of the geometry of the sine curve, not an indicator of any strange quantum nature of the light.

The experiments as planned should thus provide a striking test of QM versus local realism. In the QM corner we have Wigner densities etc and the prediction of a cosine-squared curve that is a function of thedifference in phase settingsof the local oscillators. In the local realist corner we have classical theory, slightly augmented by some experimentally-inspired ideas about phase relationships in PDC processes, and the prediction of essentially a step function but one that depends onboth local oscillator settings separately, not on their difference.

Incidentally, the same setup could very conveniently be adapted to illustrate the operation of the usual "detection loophole". It is absent in the proposals since the difference in output voltages always havesomevalue, so that you always get, when you "digitise" it, either +1 or -1. There are no "non-detections". But you could instead look at the raw voltages ...

For my paper on the subject, see:

Caroline H Thompson, “Homodyne detection and parametric down-conversion: a classical approach applied to proposed “loophole-free” Bell tests”, http://freespace.virgin.net/ch.thompson1/Papers/Homodyne/Homodyne.htm, or, in two-column format, http://freespace.virgin.net/ch.thompson1/Papers/Homodyne/homodyne.pdf (January 2005)Caroline

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# Loophole-free Bell tests

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