Exa 5

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ A.5}$

For each of the states $\ket 0$, $\ket -$, and $\ket \i = \frac{1}{\sqrt 2}(\ket 0 + \i\ket 1)$, give the matrix for the corresponding density operator in the standard basis, and write each of these states as a probability distribution over pure states. For which of these states is this distribution unique?