Okay, hello, welcome.

So today I want to finish the chapter about the experimental Bell tests.

And you remember we have discussed things like atomic cascades where you emit a photon

pair, parametric down conversion where you also emit a photon pair, or Bell tests using

ions where you exploit the high detection efficiency.

And I want to finish this chapter by discussing what people call loopholes.

And that means that all of these experiments are not quite perfect like they should be

for an ideal Bell test.

And therefore, strictly speaking, they do not yet convincingly rule out the existence

of local hidden variable theories that could underlie quantum mechanics.

So let us discuss these loopholes.

So essentially there are two loopholes.

And the first one is simply the locality loophole and the other one is the detection loophole.

So the locality loophole comes about in any experiment where you do not guarantee that

there is no sub-luminal signal possibly traveling from one detector station to the other and

telling one detector what has been the setting that you just chose at the other detector.

So in order to fix this locality loophole, simply you have to have a large distance and

be able to set your detector settings very fast and to detect very fast.

Because then there is no way that even a light signal could possibly arrive in time at the

other detector.

So in order to close this locality loophole, what we really need is simply that the travel

time of light during the time it takes to do the measurement is smaller than the distance

between the two detection stations because then there can be no signal.

For example, we learned that this locality loophole in particular is enclosed in those

biometric down conversion experiments where you have this 400 meter separation of A and

B on the Innsbruck campus.

So the other loophole then that remains in those experiments is the detection loophole

because things are not as perfect as you would like them to be.

In fact, typical photo detectors only have on the order of a few dozen percent photo

detection efficiency and then there is still only efficiency associated with collecting

these photons.

So overall you have relatively low efficiencies of actually detecting a pair of photons.

And so in order to close that in principle you would need better detectors.

And we have seen that in the example of the ion trap test experiment one has practically

perfect detection because the idea is that you have state selective resonance fluorescence

and you scatter many, many photons.

For example, in those experiments you would scatter 60 photons and even if your photon

detector is not really that efficient you can make sure that either you see all those

photons or you don't see anything and so you distinguish those two states.

The unfortunate fact remains that no one has been able so far to close both of these loopholes

at the same time.

Now I want to spend a little bit on the detection loophole.

For the locality loophole basically all you have to do is to have a large distance, that

will be very fast.

For the detection loophole we can work out a little bit what it really means, what should

be the threshold for the detection efficiency that you would need in order not to be spoiled

by the detection loophole.

And so let's go back to the Clauser-Boltron-Gimony inequality and the basic quantities that we

had here were those where you just take the outcomes at the two detection stations, let's

call them A and B and usually that would be plus or minus one and you take the correlator.