= Magic-state injection of a T gate
{title2=$|A\rangle=(|0\rangle+e^{i\pi/4}|1\rangle)/\sqrt2$}
Apply a <controlled-NOT gate> from data $a|0\rangle+b|1\rangle$ to the resource $|A\rangle$, then measure the resource in the standard basis. Outcome zero leaves data $T|\psi\rangle$; outcome one leaves $e^{i\pi/4}T^\dagger|\psi\rangle$. Both outcomes have <probability> $1/2$. Correct outcome one with $S$, using $ST^\dagger=T$, so the data has undergone the <T gate> irrespective of the measurement result. The resource is consumed, and its <Bloch vector> lies outside the <stabilizer octahedron>.
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