Let’s use a disc throwning system, where two porcelain plates are thrown at once and in different directions, one with its axis horizontal and the other vertical. To catch the plates we use a detector, made of a foam plate with parallel slots, in which the plates remain stuck. The structured foam plates are designed so well that they catch even plates with a spatial deviation of +/-45° if the plate comes perfectly centric to the slit. To the right and to the left from this point the probability reduces until it will be zero for a plate, hitting the foam detectetor in the center of the area between the slits.

Unfortunately the engineers made a joke and rotate synchronously the two mechanism for the throwing. Still the plates stay entangled. The outcomming plate 1 could be thrown in any angle and the plate 2 will be thrown by the angle of the first plate plus 90°.

For me the measurable results with the two foam plates are the same as for two optical filters and two photons from spontaneous parametric down-conversion. Noting the results of the measurements, could one see a difference between the two experiments?

In my view the results of the mechanical system with the two detectors perpendicular to each other will be:

  • in 25% of the measurement both detectors catch a plate
  • in 25% the left detector only will catch a plate
  • in 25% the same happens with the right detector an
  • in 25% no one detector catches a plate.

For me the measurable results with the two foam plates are the same as for two optical filters

In optics you have the option of rotating the axis of the analysers to test for diagonal and anti-diagonal polarizations, as well as using quarter-wave plates to test for circular polarizations (i.e. you can measure along three different bases (H/V, D/A and R/L) which are pairwise incompatible). Your system has no equivalent capacity. There is absolutely no comparison between the two.

But yes, your argument is correct in that a restricted quantum system that can only measure one single basis (instead of at least two incompatible ones) is unable to distinguish between entanglement and classical correlations.

  • $\begingroup$ Emilio, the experiment with photons from Spontaneous parametric down-conversion is such a measurement of one single basis? Do you have an example of two incompatible basises? $\endgroup$ – HolgerFiedler Nov 17 '18 at 11:13
  • 1
    $\begingroup$ @Holger It's already mentioned in this very answer. $\endgroup$ – Emilio Pisanty Nov 17 '18 at 13:04

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