Pure State
From Qwiki
In quantum mechanics, states of knowledge cannot be complete, meaning that an observer cannot know the result of all possible measurements perfectly well. However, some states of knowledge are still better than others and there remains a notion of maximal knowledge. Those quantum states of maximal knowledge are the pure states:
where the wavevector is an element of the associated Hilbert space 
. The states of non-maximal knowledge are referred to as mixed states.
Some simple relations for pure states are ρ2 = ρ and Tr(ρ2) = Tr(ρ) = 1
