Hello, I'm wondering, is it possible to define an operator on a Hilbert space that gives information about the "distinctness" of superposition components? As a simple example, imagine that we have two particles. Let |3> designate the state in which they are 3 meters apart, let |5> designate the state in which they are 5 meters apart, and |7> for seven metres apart. Now imagine the three possible states: (s1) a|3> + b|3> = |3> (s2) a|3> + b|5> (s3) a|3> + b|7> Where a and b are amplitudes such that |a|2+|b|2=1. Is it possible to define an operator that gives, say, a null result for s1 (no distinctness) while giving nonzero values for s2 and s3 and ranking them so that s3 gets a higher value (more distinct?)? If there are real quantum mechanical applications for such operators I would be very interested to learn of them. If there are no known applications even though they are nonetheless in principle definable, then I would still be very interested. Thanks!