Quantum Computing, exercise 2.1

[Genady]

Let the direction |v〉 of polaroid B’s preferred axis be given as a function of θ,  |v〉 = cosθ|→〉 + sinθ|↑〉 and suppose that the polaroids A and C remain horizontally and vertically polarized as shown. What fraction of photons reach the screen? Assume that each photon generated by the laser pointer has random polarization.

My answer is 1/2*cos²θ*sin²θ. Any objections?  

[Sensei]

Shouldn't you give the angles of each polarizing filter independently, such as alpha, beta and gamma?

Did you mean that A alpha = 0, then B "theta" (given by you), and then C gamma = 90?

 

50% of the photons will be after passing through filter A (and 50% of the photons will be reflected).

 

Edited October 7, 2023 by Sensei

[Genady]

15 minutes ago, Sensei said:

Shouldn't you give the angles of each polarizing filter independently, such as alpha, beta and gamma?

Only the relative angles matter, don't they? A and C are orthogonal, and B is at the angle θ to A.

15 minutes ago, Sensei said:

Did you mean that A alpha = 0, then B "theta" (given by you), and then C gamma = 90?

Yes, this is what they mean, I am sure.

Edited October 7, 2023 by Genady

[Genady]

Sorry, I forgot to say where the exercise came from:

Rieffel, Eleanor G.; Polak, Wolfgang H. Quantum Computing: A Gentle Introduction.