Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s3/3/2/solution

Choose the upper route for horizontal polarization, the lower route for vertical polarization, and absorb fixed optical phases into the path kets. The normalized output is
This is entanglement between two degrees of freedom of one photon. Interchanging the path convention interchanges the labels but not any probabilities.

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