A state on a C*-algebra A is a continuous linear functional φ φ : A → → C such that φ φ ( I ) = 1 (where I denotes the algebra's multiplicative identity) and φ φ ( T ) ≥ ≥ 0 for every T ≥ ≥ 0 . Such a state is called pure if it is an extremal point in the set of all states on A (i.e. if it cannot be written as a convex combination of other states on A ).