We use a different type of entangled state one where the

Question

Question: Consider the experiment of Fig.

We use a different type of entangled state, one where the photons are mutually perpendicular. That is, regardless of where a first polarizer is oriented, once a first photon is detected with a given polarization the other is found to have a polarization perpendicular to the first one. We send the mutually perpendicular polarization-entangled photons to a pair of polarizing beam splitters. The left polarizer is vertical and the right polarizer forms an angle θ with the vertical.

a. Show that the probability that the left photon gets transmitted and the right photon gets reflected is

P_V,Θ = 1/2 cos²Θ

b. What is the probability that the right photon gets transmitted and the left photon gets reflected?

c. What is the probability that the both photons get transmitted?