I got (very) confused about the concept of states, pure states and mixed states. Is it correct that a linear combination of pure states is another pure state? Can pure (and mixed) states only be expressed in density matrices? Is a pure state expressed in a single density matrix, whereas mixed states are expressed in a linear combination of several density matrices? Since a pure state is a single density matrix, a linear combination of density matrices would be a linear combination of pure states, and hence a pure state. I don't understand. I hope someone likes to illuminate me on the matter. Thanks.