Nate
What you are saying is incorrect. You can also obtain f = f1+f2+x where x contributes to for instance internal energies. So by measuring f1 does not imply that you know f2 which is an identical process to that when we have f=f1+f2. Have a look at wave mixing. There is noting strange...
I was wondering. If SPDC is caused basically by two identical coupled particles and each particle gives off a photon which is identical to its counterpart particle, but with a different spin...then why do one also get second harmonic processes (difference wave mixing) using the same crystal...