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The basic setup is described with this picture from the paper (I hope I'm allowed to link this):

So simplified quite a bit, my understanding is that the procedure goes like this:

- A single photon is sent to Bob and Alice with a ##R=50\%## probability distribution, and hence is in the state ##| \psi \rangle = |0\rangle_A|1\rangle_B + |1\rangle_A|0\rangle_B##.
- Next Alice rotates her setup by a chosen angle ##\theta##.
- Then Bob and Alice both measure their photon steams using "full quantum-state tomography using homodyne detection". I'm not very familiar with this but I assume you can't get more than one bit of information for each photon, so it must be an aggregate of many runs.
- Then when their measurements are compared it can be shown that Alice's choice of measurement angle has affected Bob's results.

If there are not simultaneous measurements by both parties, I don't see how Bob's tomography results can be binned based on the binary result from Alice, unless there is some relationship between subsequent photons.

So what's wrong with my understanding?