Ex4 11

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 4.11}$

Design a measurement on a $3$-qubit system that distinguishes between states with different numbers of $1$ bits, and gives no other information. Write all operators in bra/ket notation.