I believe that we can take a single photon state as a tensor product of a frequency Hilbert space (infinite dimension) and a polarization Hilbert space (dim 2). Does this mean we can measure the polarization and the frequency at space-like separated regions a the same time?
My second question is about frequency and polarization entanglement. If we have an entangled state between the frequency and the polarization, but we model the system as having a classical distribution over frequencies, what kinds of mistakes will we make in understanding any joint measurements of polarization and frequency? I am thinking about a channel which entangles the polarization and the frequency which we imagine is a classical channel over frequencies.