# Coincidence counting in Bell experiment

• ajw1
In summary, in a Bell experiment, the number of coincidences, or pairs of photons that are detected, is very low, and is only around 1% of the total number of photons. This is done by assuming that each photon is paired, and by sampling the data to make sure that the results are accurate.
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?

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

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)?

ajw1 said:
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%
ajw1 said:
- 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.

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## What is coincidence counting in Bell experiment?

Coincidence counting is a technique used in the Bell experiment to measure the correlations between particles in quantum entanglement. It involves counting the number of times that two particles are detected at the same time, or in "coincidence".

## Why is coincidence counting important in the Bell experiment?

Coincidence counting is important because it allows scientists to test for non-locality, which is a key aspect of quantum entanglement. By measuring the correlations between entangled particles, scientists can determine if there is a hidden connection between them that cannot be explained by classical physics.

## How does coincidence counting work?

In the Bell experiment, coincidence counting is achieved by using two detectors that are synchronized to detect particles at the same time. The number of coincidences is then compared to the total number of particles detected to determine the level of correlation between them.

## What are the results of coincidence counting in the Bell experiment?

The results of coincidence counting in the Bell experiment have consistently shown a higher level of correlation between entangled particles than what is predicted by classical physics. This supports the idea of non-locality and the principles of quantum entanglement.

## What are the potential implications of coincidence counting in the Bell experiment?

The results of coincidence counting in the Bell experiment have important implications for our understanding of the nature of reality. It challenges our classical view of the world and raises questions about the fundamental principles of quantum mechanics. It also has potential applications in quantum computing and communication.

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