Are photon probability amplitudes entangled in a two-filter setup?

[zonde]

I have thought for some time that it is physically correct to treat photon source as time evolving rather than photon state (i.e. using Heisenberg picture rather than Schrodinger picture) so I was glad to find this picture in Feynman's book (QED: The Strange Theory of Light and Matter):

In this picture (b) there is space time diagram that shows time evolution of photon's probability amplitude at source. So I confirmed for myself that the idea is fine.

But I want to go a bit further based on this diagram. Say we have light source with broad spectrum.
After light source we place narrow bandwidth filter. So we can view this filter as monochromatic light source where photon probability amplitude undergoes coherent evolution.
But after this filter we place another identical filter that becomes new monochromatic light source. It has to undergo time evolution coherently with the first filter, right? Or in other words are they entangled?
This is the question I wanted to ask.

 

[Jilang]

Are you asking if the sources are entangled or the photons are entangled?

 

[zonde]

Are you asking if the sources are entangled or the photons are entangled?

I am asking about sources (filters). We could talk about single photon in this example so there is no point talking about photon entanglement.

 

[Jilang]

I should say so then, at least once the light had arrived at the second filter.