The state of the universe determined everything. A quantum system is a subsystem of the universe. Hence it is at time ##t## in the state determined by the corresponding reduced density matrix at time ##t##. These are the allowed states of quantum systems.If so, then how to know in general which superpositions are allowed and which are not?
If you are able to prepare a particular spin state (a superposition, say), it means that at the time of preparation, the state of the universe is such that the reduced density matrix of the spin is in this state. (See post #22 for full details.)
In a similar way, all preparable and all measurable information give little bits of information about the state of the universe, and from this information, one can draw theoretical conclusions.