 But the assignment of states to systems in quantum mechanics seems not to conform to these expectations (see related entry  quantum mechanics).  Recall that the quantum state of a system specifies its chances of exhibiting various properties on measurement. At least in ordinary quantum mechanics, the mathematical representative of this state is an object defined in a Hilbert space—a kind of vector space. This is analogous in some ways to the representation of the state of a system of particles in classical mechanics in a phase space. Let us formulate a principle of