 Quote by rq704c
If you have two momentum entangled photons, one heading down axis "a" and the other down axis "b" and you destroy all the axis "a" photons by measuring their position, all the axis "b" photons should not interefere with themsselves because you have forced them into a postion definite state. Setting up a double slit on axis b and observing no intereference would be a good indication the other photons are being measured given most of the photons are being down converted and are entangled.
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The flaw in this scheme is exactly, what I explained in my last post. See page 46 of the Dopfer thesis for a detailed explanation. To cut it short single photon interferences and coincidence count interferences are complementary. If you have coincidence count interferences, you can do position measurements, but there is no single photon interference pattern to destroy because the light source in this single arm is too incoherent to produce an interference pattern.
On the other hand, if there is a single photon interference pattern in one arm, this means automatically, that the momentum entanglement is already destroyed and the two photons behave like independent photons. You can imagine this as happening due to the strong decrease in possible directions (or k-vectors) for the photon as you increase the distance between the crystal and the double slit. As mentioned before this decrease destroys the coincidence count interference pattern, which is a measure of the degree of entanglement.
This is not a consequence of the geometry, but a general problem. You want to have as few k-vectors as possible to enlarge coherence, but you need many k-vectors to achieve meaningful momentum entanglement.
The references 23-25 in the Dopfer thesis also discuss this problem a bit.