Observables on the "3 polarizers experiment"

[DougFisica]

TL;DR

Analogy between 3 polarizers experiment and Stern-Gerlach experiment

Observables on the "3 polarizers experiment"
Hi guys,

I was analyzing the 3 polarizers experiment. This one: (first 2 minutes -> )

Doing the math (https://faculty.csbsju.edu/frioux/polarize/POLAR-sup.pdf) I realized that the process is similar to the Stern-Gerlach' experiment.

Using spins for the Stern Gerlach experiment: if you prepare a spin up (Z component) sample (first filter), and pass it to a second filter that measure the X component of the spin. You lose information about the Z component.

I undertand that Z and X component are non-commuting observables.

My question is:

Is there there an analogy for the polarizers experiment?

For example, if I measure the vertical component (first polarizer), I cannot get information about the 45º component (second polarizer).

I would guess the answer is Yes, however I cannot understand the "45º component" physical meaning.

 

[Nugatory]

For example, if I measure the vertical component (first polarizer), I cannot get information about the 45º component (second polarizer).

I would guess the answer is Yes, however I cannot understand the "45º component" physical meaning.

What you are calling “the 45º component” is the probability amplitude that the photon will pass through a filter oriented at 45 degrees. No matter what that amplitude was before the vertical polarizer (it could even have been 1, if the photon had previously passed through a polarizer at 45º) the vertical measurement leaves that amplitude at $\sqrt{2}/2$ - we no longer know anything about the previous state and the photon has a 50% chance of passing a 45º filter.

To continue the analogy with the Stern-Gerlach measurement: just as the particle state “spin up” can be written as the vector sum of the states “spin left” and “spin right”, the vertically polarized state of a photon can be written as the vector sum of the states “polarized at 45º” and “polarized at -45º“.

 

[DougFisica]

Thanks for the answer =)