# Efficiency model in loophole free photon Bell tests

1. Jan 13, 2016

### 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.
Code (Text):
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.

2. Jan 19, 2016