I understand the classical model of light polarization in terms of two complex numbers, known as Jones vector.
In the quantum case, for example, consider photons sent through two polarizers, the first one at an angle $\theta$ with the second one, aligned on the $x$-axis (perpendicular to the $y$-axis).
According to The Feynman Lectures on Physics, vol III, § 11-4, the state vector of a photon passing the first polarizer is $$\cos\theta\ |x\rangle+\sin\theta\ |y\rangle,$$ where $|x\rangle,|y\rangle$ are the state vectors of photons polarized along $x,y$-axes.
Similarly, the state vector of a right polarized photon is $$\cos\theta\ |x\rangle+ \exp(i\ \pi/2)\ \sin\theta\ |y\rangle,\theta=\frac{\pi}{4}$$
Why is it so?
The moduli of coordinates are the square roots of the probabilities of transmission, $\cos^2\theta,\ \sin^2\theta$, set by classical electrodynamics.
But how are the coordinate phase differences ($y$ less $x$, $0$ in the first case, $\pi/2$ in the second case) determined?
They are just taken from the classical case: the quantum state vector is identified with the classical Jones vector.
Can it be justified from symmetries in the 2D Euclidean space $(x,y)$, where the electrical field lies?
Is it a theorem in quantum electrodynamics?
