(a) A vertically polarized photon goes through two polarizing filters, the first of which is vertically aligned and the second at degrees. What is the probability that the photon is transmitted through both filters?

(b) Now, you are allowed to place a polarizing filter between the two filters in the previous question. If you wish to maximize the probability that the photon is transmitted through all three filters, what angle would you orient the additional filter? Here, assume that a 0degrees filter corresponds to a horizontal filter and 90degrees a vertical filter. Provide your answer in degrees as a real number between 0 and 90 .

(c) In that case, what is the probability that the photon is transmitted through all three? Round your answer to the nearest thousandth. (ex: 0.182)

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(a) 0.5

(b) 67.5
(c) 0.7285

We have a qubit in the state |ψ>= √3/2 |0>+ 1/2 |1>, which we want to measure in the {Cos θ |0> + Sin θ |1>, Sin θ |0> - Cos θ |1>} basis. In order for the two possible outcomes to be equiprobable, what should be the value of θ in degrees? (Answer between 0 and 90.)

any answers for this?

answer : 0.5

answer : 75

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(a) To determine the probability that the photon is transmitted through both filters, we need to consider the effects of polarization on each filter.

The first filter is vertically aligned, which means it only allows vertically polarized light to pass through. Since the photon is vertically polarized, the probability of it passing through the first filter is 1.

The second filter is oriented at a certain angle (let's call it θ), which affects its transmission properties. The angle θ is not specified in the question, so the probability of the photon passing through the second filter depends on θ.

In general, the probability of a photon passing through a polarizing filter at angle θ is given by Malus's law:

P = cos²(θ),

where P is the probability and θ is the angle between the polarization direction of the incoming photon and the transmission axis of the filter.

Therefore, the probability that the photon is transmitted through both filters in this case is P = 1 * cos²(θ).

(b) In order to maximize the probability of the photon being transmitted through all three filters, we need to consider the orientations of the filters. We already have a vertically aligned filter as the first one.

For the additional filter placed between the first and second filters, we need to find the angle θ that maximizes the probability P = cos²(θ). Since the maximum value of cos²(θ) is 1 (when θ = 0 or θ = 90), we want to align the additional filter either vertically or horizontally.

To maximize the probability, we should choose the orientation that matches the initial polarization of the photon, which is vertical. Therefore, we should align the additional filter vertically (θ = 90 degrees).

(c) With the additional filter aligned vertically (θ = 90 degrees), the probability that the photon is transmitted through all three filters is:

P = 1 * cos²(90) * cos²(θ).

Since cos²(90) = 0, the overall probability becomes 0. Therefore, from the given configuration, the probability of the photon being transmitted through all three filters is 0.