Hello, I have a few questions about this interferometer setup, see attached picture. The beamsplitters are 50/50 and the setup is symmetric. initial |i> first beamsplitter, where U is unitary and represents the beamsplitter. U|i> = 1/sqrt(2)( |u> + exp(ix)*|d> ) second beamsplitter, A and B are detectors (upper and lower) U|d> = 1/sqrt(2)( |A> + exp(ix)*|B> ) U|u> = 1/sqrt(2)( |A> + exp(iy)*|B> ) now what is x and y? I let x = 0 and then assume that <d|u> = 0 and use this to determine y under the assumption that U is unitary this gives y = pi. U|d> = 1/sqrt(2)( |A> + |B> ) U|u> = 1/sqrt(2)( |A> - |B> ) this gives the state after the second beamsplitter to be 1/sqrt(2)( 1/sqrt(2)( |A> + |B> ) + 1/sqrt(2)( |A> - |B> )) = |A> and this gives probability of detection in A to be |<A|A>|^2 = 1 and B |<B|B>|^2 = 0 I have questions about this experiment. 1. How come its valid to assume that |u> and |d> are pure states? 2. Will the experimental outcome be different if we put up a wall on the horizontal symmetry line? Or wont that affect the experiment cause all the interference takes place at the second beamsplitter? 3. is possible to view the |u> (and |d>) as being pure states because they are sort of statistically pure as long as the paths are separated well enough? Has this anything to do with the statistical interpretation of QM ?