Sunday, 3 July 2011

On the fair sampling

Real EPR experiments with photons are performed using a lot of restrictions on the counting process:
  • There is always a large amount of background noise (single photons, accidental doubles)
  • A time windows is used: only clicks that are found on both sides (Alice and Bob) within the time window are considered to be entangled.
  • Often it is the electronic logic that separates 'entangled pairs', so the 'others' don't even enter the raw data.
  • Detectors mostly have low efficiency. For example in the well known Weihs experiment (1) this was 5% (Detectors have been improved since then).
Caroline Thompson has written a critical article (2) about the sample efficiency in the famous experiment of Aspect and of others. Alain Aspect had to subtract 25% of his coincidences to get his QM confirmed. Furthermore without this subtraction she shows the results follow the classical expectation. Considering all this it hardly seem fair that local realistic models should count most of the photons.

Nevertheless realistic models that allow a fraction of misses (I call them class A models*) I have found are able to produce QM like results using about 70% (3, 4) of the pairs. The Adenier model (3) is just for demonstration purposes, Ashwanden has a model based on a realistic hypothesis of the behavior of the elements involved in an EPR experiment.

Based on the description of Adenier (unfortunaly the exact details of their model is not in the article) I was able to quickly reproduce a model using 47% of the photon pairs. I have included it in the software.

  1. Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, and Anton Zeilinger, Violation of Bell’s inequality under strict Einstein locality conditions,
  2. Caroline H Thompson, Subtraction of “accidentals” and the validity of Bell tests,
  3. Testing the Fair Sampling Assumption for EPR-Bell Experiments with Polarizing Beamsplitters, Guillaume Adenier and Andrei Yu. Khrennikov, Video:
  4. Manuel Aschwanden, A classical view of quantum entanglement,
* Class A models normally only prove that real experiments can be explained using a LHV model. Only with high efficiency (>83 % i think) they could also disprove Bell.

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