Ex10 26

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 10.26}$

Show that if $\{\ket{x_i}\}$ is the set of possible states resulting from a measurement and $p_i$ is the probability of each outcome, then $\rho = \sum p_i \ket{x_i}\bra{x_i}$ is Hermitian, trace $1$, and positive.

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