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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!

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.

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The reason for my partial answer and my comment is that I'm not sure what "quantum noise" means in this context, and because the group is about signal processing it's out of scope to expect someone (i.e. me) to know enough quantum mechanics to know whether your "quantum" noise has some deeper meaning, or is just a Poisson process.

DSP is about doing math on signals that have known mathematical properties. So strictly speaking, DSP is totally about starting with a signal that has known mathematical properties -- or at least it has mathematical properties whose unknowns are bounded in a firmly known way. Technically, DSP folk know nothing about the signal "out there" (but often they do -- see below).

It's reasonable to expect at least some (but not all) DSP folks to have a pretty good idea of how a signal received by an ordinary terrestrial radio, or over an ordinary terrestrial phone line, or by an ordinary electronic camera might behave, because that covers a lot of what DSP folks do in practice.

As an example: I'm working a lot with imaging these days, and if you're working with low return levels then you run head-on into a "quantum noise" effect. To wit, a photon striking a pixel has a certain probability of knocking an electron loose, and that electron has a certain probability of getting collected into the pixel's capacitor (the product of those two probabilities is the detector's "quantum efficiency", by the way).

If your "quantum noise" just means that you have a detector that, one way or another, counts photons -- great. That's easy enough that I can understand it after you state that clearly in your question. I know that I'm dealing with a front-end that has a Poisson process followed by some random noise process (analog to digital converters always have some random noise), and I can deal with that.

However, if your "quantum noise" has some quantum mechanical solution* then I can't help you, because that requires a knowledge of quantum mechanics -- and quantum mechanics is the purview of physicists, not DSP experts. Also -- and forgive us if we didn't state it -- but your question boiled down to "read a bunch of impenetrable academic papers that are totally out of your specialty and give me a read on what they mean in this context". That's pretty much out of scope of any group at any time. It's up to you to excerpt the juicy bits, and maybe interpret them.

I can't tell you, as a DSP person, whether aiming the 1550nm laser ten microradians to the right is going to reduce the "quantum noise", or whether adding another Josephine junction will do the same. That's not DSP, that's quantum physics.

On the other hand, if you give me ten incoming signals and you tell me how they correlate or even give me someone else's equation on how they correlate, then I may be able to tell you how to extract useful information from them, because that is DSP.

Again, asking a DSP person to read a paper by an astrophysicist to work out the quantum mechanics of their device to determine if the resulting problem is quantum mechanics or just signal processing is out of scope -- but saying what the signal looks like as a mathematical entity and then asking a question about it is in scope. Ditto, asking a DSP person to read a paper about cardiology to determine how to evaluate an EKG for a person's health is out of scope, but telling us what the signal looks like as a mathematical entity, and how it looks different when someone is sick and then asking how to sort it out is in scope.

If you need someone to read all those papers for you and say "oh, well, that just boils down to signal processing" that's the job of a physicist or whoever wrote the papers. Once you can say in your question that (A) it's just signal processing, and (B) the nature of the signal to be processed, then it's a question for a signal processing group.

* e.g. if there's something you can do with gallons of liquid helium and lasers and exotic detectors that lets you squeeze the noise (e.g. the phase-noise quantum squeezing that they've put into LIGO, where they get better phase noise performance at the expense of higher amplitude noise).

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  • $\begingroup$ Thank you for your thorough discussion! I haven't singled out a specific user and asked them to answer, and I was surprised that you posted an answer before your "circular question" comment could even be addressed. Answering is always optional. I certainly learned something new; that heterodyning preserves phase and not time as I'd originally thought, and that even by itself is helpful. So I'm wondering if I should rewrite the question and narrow it down such that your answer answers it, splitting the rest to a future question or not. I'll wait to see if additional answers provide advice. $\endgroup$
    – uhoh
    Commented Apr 10, 2022 at 1:00
  • $\begingroup$ Quantum mechanics isn't a complete stranger to the questions and answers here, nor are discussions of what causes various kinds noise and how that relates to processing. Also the site's What topics can I ask about here? begins "Signal Processing Stack Exchange is for practitioners of the art and science of signal, image and video processing." and lists Conceptual questions, Theory questions, Practice questions, Algorithm recommendations, Algorithm debugging questions, and even Homework question. Neither the term "digital" nor "DSP" is mentioned. $\endgroup$
    – uhoh
    Commented Apr 10, 2022 at 1:02
  • $\begingroup$ As far as I can tell analog processing is just as on-topic here as digital processing. $\endgroup$
    – uhoh
    Commented Apr 10, 2022 at 1:04

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