Coincidence counting in Bell experiment

[ajw1]

I have trouble finding the following information on the coincidence counting in a Bell experiment:
- Is there a fraction of single photons (not entangled) produced in the experiment and how are the final results corrected for this?
- No-hits on both side can never be counted (nothing is measured). How is this handled?

 

[DrChinese]

Yes, there are photons that show up as singles. These are discarded. In fact, most detections fit this criteria. The number of detections per second might be on the order of 5000 each for Alice and Bob. The number of pairs (coincidences) is about 1% of that, or about 50 per second.

The pairing of hits is done by creating a time window. This is typically on the order of 20-40 nanoseconds - there are about 30 million such windows in a second. Since detections run about 10,000 total per second, you can see that less than 1 in 1000 time windows has anything at all going into it.

If you increase the size of the time bin, you get more coincidences but you also increase the chances of pairing photons that are not entangled. If you decrease the size of the window, you may exclude some entangled pairs. So there is a balance.

You may benefit from this article, see table 1 on page 7:

http://arxiv.org/abs/quant-ph/0205171

 

[ajw1]

Thanks for your answer.

So one only needs the coincidences, corrected by the possibly false hits (two single photons within the time frame) to show the violation of the Bell inequality (I had just read a proof of the Bell inequality based on the full outcome space)?

 

[zonde]

I have trouble finding the following information on the coincidence counting in a Bell experiment:
- Is there a fraction of single photons (not entangled) produced in the experiment and how are the final results corrected for this?

It is assumed that source produces photons always in pairs and there seems to be no reason to doubt that.
However signal can be diminished while it gets to polarizer.
As well detectors can be tuned to detect more or less photons.
For example in this experiment:
http://arxiv.org/abs/quant-ph/9810080"
detection efficiency reported was 5%

- No-hits on both side can never be counted (nothing is measured). How is this handled?

Fair sampling assumption is used here to make some conclusions about undetected pairs.
It means that photon sample detected is faithful representative of photon sample you have after polarizer.
Without that Bell inequalities are not applicable to photon entanglement experiments.