So in many sources I have read that
A pure state contains only one element, since the only entry on the
density matrix will be 1.
But what about superpositions?
I mean a state like
$$\mid \psi\rangle = \alpha\mid0\rangle+\beta\mid1\rangle$$
for example is a pure state but it's corresponding density matrix can have 4 non-zero elements.
Why is it that these definitions seem to ignore superpositions?
