I ran across this statement in a professor's notes and I think it's just a typo, but I wanted to take the opportunity to check my understanding. So in his notes it says:
even if we have complete knowledge of quantum systems, they still can be in the[a] mixed state
As far as I understand, a mixed state is simply a classical mixture of quantum states. If we inherit the definition of maximum information from the von neumann entropy, then we should define maximum information to correspond to an entropy of ln(1) = 0. But since the density matrix is not a rank 1 projector in a mixed state, this condition is not met. Is there some other notion of maximum information that I am not aware of, do I have some misunderstanding, or is this just a typo?