In quantum mechanics a state is described by a ray in a Hilbert space, and an observable by an Hermitian operator acting on that Hilbert space. After measurement, the state collapses to an eigenstate of the operator representing the measurements. The probability of any outcome is given by the Born rule.
Erm, that might not have been all that clear. Let me rephrase that: in quantum mechanics, the state of the system represents, well, the state of the system (a rare occasion in physics when the term used makes any sense, and even has some relation to the idea it signifies). This means basically all the information specifying the contingent facts about the particular history of the system in question. This leaves only the question of accessing that information.
Shores of the Dirac Sea 