Today I came across a paper, "Experiments testing macroscopic quantum superpositions must be slow," by Mari et al., which proposes and analyzes a thought experiment involving a first mass mA placed in a position superposition in Alice’s lab, the mass mA producing a gravitational field that potentially affects a test mass mB in Bob’s lab (separated from Alice’s lab by a distance R), depending on whether or not Bob turns on a detector. The article concludes that special relativity puts lower limits on the amount of time necessary to determine whether an object is in a superposition of two macroscopically distinct locations (versus a mixed state).
But the problem is that, as far as I understand, there is no way to determine whether an object is in a superposition at all (versus a mixed state)!
A superposition is determined by doing an interference experiment on a bunch of “identically prepared” objects (or particles or masses or whatever). The idea is that if we see an interference pattern emerge (e.g., the existence of light and dark fringes), then we can infer that the individual objects were in coherent superpositions. However, detection of a single object never produces a pattern, so we can’t infer whether or not it was in a superposition. Further, the outcome of every interference experiment on a superposition state, if analyzed one detection at a time, will be consistent with that object not having been in superposition. A single trial can confirm that an object was not in a superposition (such as if we detect a blip in a dark fringe area), but no single trial can confirm that the object was in a superposition. Moreover, even if a pattern does slowly emerge after many trials, every pattern produced by a finite number of trials – and remember that infinity does not exist in the physical world – is always a possible random outcome of measuring objects that are not in a superposition. We can never confirm the existence of a superposition, but lots and lots of trials can certainly increase our confidence.
In other words, if I’m right, then every measurement that Alice makes (in the Mari paper) will be consistent with Bob's having turned the detector on (and decohered the field) -- thus, no information is sent! No violation of special relativity! No problem!
Am I wrong? Is there a way to test whether a particular object is in a coherent superposition? If so, how? If not, then why do so few discussions of quantum superpositions mention this?