Photons and uncertainty principle Let's assume we have a perfect single-photon source: a device emitting exactly one photon at a time, with defined energy and direction. Let's shoot a photon: we know exactly the position of the photon (starting point and time, velocity) and it's momentum (energy and velocity). Would such a device violate uncertainty principle? Where is the trap?

Just to clarify things, my question essentially is: a particle (e.g., a photon) prepared in an eigenstate of momentum can be found everywhere (at least along the direction of momentum)?
 A: In your post when you say you 'know' the position and momentum of a single photon you really don't know anything, you are just making a prediction, not making a measurement. In your head you are basically assuming classical physics and using the initial parameters of the system to calculate the final parameters. In order to actually know any properties about a system you will have to perform a measurement, and to really say anything conclusive you will have to do this many times. Take your single photon source and measure the momentum and position of the outgoing photons numerous times - the product of the standard deviation in momentum and position will be greater than $\frac{\hbar}{2}$. 
A: Interesting question that leads to:

a particle (e.g., a photon) prepared in an eigenstate of momentum can be found everywhere (at least along the direction of momentum)?

No. Per MC Physics, the photon has physical presence at one location. Your understanding may be confused because the first uncertainty of measuring a photon comes from the exact emission source position and the EMF field at time of emission (giving it velocity and frequency). The second uncertainty comes from the exact distance from the source to the atoms in the detector. Assuming travel in a vacuum. The third uncertainty is the exact rotation position (from frequency at the initial emission) of the mono-charges in that photon at time of interacting with those atoms in the detector. 
