= Measurement of linear photon polarization
{title2=$M(\phi)=\cos2\phi\,Z+\sin2\phi\,X$}
With $|V\rangle=|0\rangle$ and $|H\rangle=|1\rangle$, an analyzer oriented at angle $\phi$ from vertical has positive-outcome state $\cos\phi|0\rangle+\sin\phi|1\rangle$. Subtracting the two orthogonal rank-one <projection operators> gives $M(\phi)=\cos2\phi\,Z+\sin2\phi\,X$, where $X,Z$ are <Pauli operators>. Physical polarization angles are therefore half their corresponding <Bloch sphere> angles.
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