The breadth of the diffraction pattern says that the photon has a certain probability of illuminating each of them, and until we measure which one, all amplifiers must be considered to be viable options.

Yes, but we humans are not the only certified observers in the universe.

An optical amplifier is a perfectly good photon detector, and putting a photon into a laser amplifier "collapses the wave function", so that the photon appears in one and only one optical amplifier, which will multiply it up to (say) 10

^{6} photons.

This is one of the principles of quantum cryptography - if someone attempts to copy the entangled photons by means of beam splitters or optical amplifiers, the entanglement is lost. It is also why quantum cryptography is a nuisance, because you have to use "dark" fiber, which severely limits the range of the encrypted stream.

As I understand it, just because the gain of an optical amplifier can be 10

^{6} does not mean that a 1 in 10

^{6} chance of detecting a photon will be multiplied up to just 1 photon.

What it means is that if you make 10

^{6} trials with

*different* single photons, there is an even chance of detecting a burst of 10

^{6} photons from this particular optical amplifier.