Ex10 5

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.5}$

We showed that any density operator can be viewed as a probability distribution over a set of orthogonal states. Show by example that some density operators have multiple associated probability distributions, so that in general the probability distribution associated to a density operator is not unique.