Why can't quantum phase noise in radio astronomy amplifiers just be filtered out after down conversion, instead of down-converting first? asks (somewhat naively1 perhaps) about quantum phase noise. The scope of the question is perhaps too big for a single question - I didn't realize that in the beginning, but since @TimWescott quickly posted a partial answer while at the same time suggesting the question was circular and perhaps unclear, I'm not sure if I should refine and narrow the question to match their current simple answer based on a trigonometric identity and separate out the rest for a new question or not.
Below @TW's answer is a comment with the correct formula and @TW has commented:
I'm not touching the "quantum phase noise" because this is a DSP group, and "quantum" is about physics. So if the "quantum" part is retained, through demodulation, somehow (i.e., if quantum states stay entangled, and how you demodulate it either retains the entanglement or destroys it), then that's physics, not signal processing.
Which makes what I should do next even more complicated because I'm not sure if the comment asserts that quantum phase noise can not be address with signal processing or not.
note: The basis of my questions and the sources I site refer to the signals in radio telescope arrays, such as the Atacama Large Millimeter Array for example. To the extent of my understanding, there is no deliberate entanglement involved in the way these receivers work. Sources just mention "quantum noise" and that may be simply $K_B T$ related but have nothing at all to do with entanglement.
I'm pretty confident discussing of physics or at least physical processes that generate noise isn't purely persona non grata here in DSP SE, but I'm not sure, and @TW doesn't cite any site policy or link to some consensus in meta that questions asking about addressing quantum phase noise via signal processing is off topic.
For example, if it's known that quantum phase noise can't be addressed via signal processing, then that seems to be an excellent answer to my question about filtering quantum phase noise, doesn't it?
1Phase noise in general (quantum or not) in signals is a new concept for me; it's likely I'm going to keep plugging along on my own slowly to better understand it. It turns out I will need to address phase noise in the 2D interference lattice (sometimes called moire patterns) produced by two real world near-periodic lattices (due to local forces and defects) in the future. So have patience as I seem to bounce back and forth between understanding and not understanding aspects of noise!
- determining if a coincident point in a pair of rotated hexagonal lattices is closest to the origin?
- Proposing a 2D quasicrystal; what are the necessary and sufficient conditions? (If it looks like a duck and quacks like a duck, or...?)
There's also a chat room with links to several answers which address conventional(?) phase noise in this chat room but it was locked fairly quickly. For some reason I didn't see the last notification. I've asked here that it be unlocked (rather than continuing the discussion in comments again) but so far perhaps nobody has seen my request.