Ex10 4

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.4}$

Distinguishing pure and mixed states.

a) Show that a density operator $\rho$ represents a pure state if and only if $\rho^2 = \rho$. In other words, $\rho$ is a projector.

b) What can be said about the rank of the density operator of a pure state?