Ex4 17

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 4.17}$

a) Show that any state resulting from measuring an unentangled state with a single-qubit measurement is still unentangled.

b) Can other types of measurement produce an entangled state from an unentangled one? If so, give an example. If not, give a proof.

c) Can an unentangled state be obtained by measuring a single qubit of an entangled state?