You raise an interesting point, and you're right that quantum treatment is not necessary in the regime where many light particles pass through the circuit, in w

You raise an interesting point, and you're right that quantum treatment is not necessary in the regime where many light particles pass through the circuit, in which case we can talk about light as a continuous thing, that can be infinitely subdivided. A quantum treatment of polarization is only required in the single-photon regime. Specifically consider an experiment where a light beam passes through three polarizing filters: first a horizontally-polarizing lens H, then a diagonally polarizing lens D, and finally a vertically polarizing lens V. photons ------> H ----> D --> V -> The result of this "triple filtering" for a beam of light (consisting of gazillions of photons, modelled as a continuous wave) can be explained as the wave amplitude being "projected" along the polarization axis of each lens. At each polarization step the projection angle is 45 degrees, so the wave intensity is reduced by cos(45)=1/sqrt(2) which is equivalent to a reduction in optical power of 1/2. The power of the beam that passes through all three lenses is 1/4 of the power leaving the first lens. No need for quantum, since we model the beam of light as a continuous quantity that can be infinitely subdivided. If we repeat the same experiment sending one photon at a time however, we can't say "the photon divides" since by definition a photon is the smallest possible quantum of light. There is not such thing as 1/sqrt(2) of a photon. Basically, when a H-polarized photon reaches a D-polarizing lens, a classical physicists is forced to pick whether the photon goes through, or is reflected—the option "partially goes through" is not allowed. It's only in this regime that the "photon is a wave" explanation fails. The quantum explanation uses a probabilistic approach and explains the probability of a H-polarized photon going through the D-polarizing lens is 1/2 and subsequently the (now D-polarized photon) going through the third V-polarizing lens is also 1/2 so the overall probability of passing through all three lenses is 1/4.