= Solution
For a fixed propagation direction and spatial mode, a <photon> has two independent <transverse polarization> <Amplitude>[amplitudes]. Orthogonal horizontal and vertical states span its two-dimensional <Hilbert space>: $\alpha|H\rangle+\beta|V\rangle$, with $|\alpha|^2+|\beta|^2=1$. <polarization (waves)>[Polarization] analyzers measure bases in this space, and <Phase plate>[phase plates] implement transformations of its relative <Amplitude>[amplitudes]. Additional spatial or <frequency> modes enlarge the space and must not be silently discarded.
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