Ex11 3

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 11.3}$

Show that the code $C_{PF}$ of section \ref{phaseErrors} corrects all linear combinations of single-qubit phase-flip errors $\{I, Z_2, Z_1, Z_0\}$ on any superposition $a\ket{\tilde 0} + b\ket{\tilde 1}$.