Efficiency model in loophole free photon Bell tests

[zonde]

I would like ask comments about assumed photon detection efficiency model used in these experiments that test Bell inequalities and consequences if it does not hold.
http://arxiv.org/abs/1511.03189
http://arxiv.org/abs/1511.03190

Detection efficiency is calculated as two-fold coincidence events divided by singles counts (from one side). That method assumes equal nondetection probability for all photons. But if we have different nondetection probabilities some error estimates would come out different.

I made a simple mathematical test. I compare single sample with identical detection probabilities for all photons and another sample that consists of two subsamples where one has 100% detection probability and the other one has 25% detection probability.

True sample size    single detections    coincidences    detection efficiency
Sample 1
160                        120               90              90/120=75%
Sample 2
80                         80                80              80/80=100%
160                        40                10              10/40=25%

Notice that average efficiency for sample 2 would come out the same as for sample 1 as single counts and coincidences sum up to the same numbers as in sample 1.

From this example it seems that if detection efficiency model does not hold we can underestimate true sample size and that can spoil some error calculations e.g. double photon rate.

 

[eljose79]

Thank you for bringing up this important issue. The assumed photon detection efficiency model used in experiments testing Bell inequalities is a crucial factor in accurately interpreting the results. As you have demonstrated in your mathematical test, if the model does not hold, it can lead to underestimation of the true sample size and potentially affect error calculations.

It is important for researchers to thoroughly validate and calibrate their detection efficiency models to ensure accurate results. This can be done through careful experimental design and analysis, as well as using control samples with known detection probabilities.

In addition, it is crucial to clearly report and discuss the assumptions and limitations of the detection efficiency model used in the experiment. This will allow for a better understanding of the potential impact on the results and any necessary adjustments or corrections that may need to be made.

Overall, it is important for scientists to be aware of and carefully consider the assumptions and limitations of any models used in experiments, and to continuously strive for accurate and reliable results. Thank you for bringing attention to this issue and for your contribution to the scientific community.