Conditional path probabilities after a quarter-wave plate
= Conditional path probabilities after a quarter-wave plate
A detected lower-path <photon> with vertical <polarization> evolves under an angle-dependent <Jones matrix>. For fast-axis angle $\eta$, its horizontal <amplitude> is $(1-i)\sin\eta\cos\eta$ and its vertical <amplitude> is $\sin^2\eta+i\cos^2\eta$. A later vertical-path <probability> therefore depends on the plate orientation and on whether the earlier lower-path event has been conditioned on.