quantum mechanics - Can we determine whether a photon's polarization is fixed or in a superposition

Say you have a photon source that produces two kinds of photon,

• a photon in a superposition with respect to polarization, |H> + |V>; and


• a photon whose polarization is not in superposition, |H> OR |V>

The photon source randomly decides which type to output. Also, when outputting a photon which is not in superposition, the polarization is random. Is it possible to detect whether a photon's polarization has been measured?

Thanks for the help so far. I've refined the question and, in doing so, it may present "a moving target" - apologies for that!

I gather (from what I've read) that it's not considered possible. If I understand correctly, "the test" would require many photons to interfere with themselves before a statistical analysis would reveal whether they were in a superposition or not; so "testing" a single photon doesn't provide enough data for a statistical conclusion(?)

At this point I've tried to improve the question so that it's less ambiguous to those who have a better understand of the subject. Actually I'm afraid of introducing ambiguity through use of symbols and/or terms which I dont really understand. It's also quite possible that I'm incapable of understanding the answer to my question! (Thanks Emilio, you may be correctly anticipating the reason for my question , though you're loosing me with "reference frames" and "basis states").