We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of
eigenstates of an observable, and develop some signatures for their existence.
We define the extent, or size S of a superposition, with respect to an
observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that
superposition. Such superpositions are referred to as generalized S-scopic
superpositions to distinguish them from the extreme superpositions that
superpose only the two states that have a difference S in their prediction
for the observable. We also consider generalized S-scopic superpositions of
coherent states. We explore the constraints that are placed on the statistics
if we suppose a system to be described by mixtures of superpositions that are
restricted in size. In this way we arrive at experimental criteria that are
sufficient to deduce the existence of a generalized S-scopic superposition.
The signatures developed are useful where one is able to demonstrate a degree
of squeezing. We also discuss how the signatures enable a new type of
Einstein-Podolsky-Rosen gedanken experiment.Comment: 15 pages, accepted for publication in Phys. Rev.
