Let me base the discussion on the pictorial description of the delayed choice quantum eraser experiment on wikipedia.
First suppose that we do precisely the same thing with the lower parts of the blue and red beams as we do with the upper parts, i.e. we put them through a lens which ends at a new detector $E_0$.
Question. Would there be the interference pattern at $D_0$ (or - I suppose equivalently - at $E_0$)? If there woudn't be - why?
I thought there would be, but then it occured to me we could use it to communicate faster than light - by shooting the lower parts of the red and blue beams to a distant partner. Then the partner would send the mesage either by preparing the setup above (and so causing the patterns at $D_0$ to interfere), or by preparing the setup of the original delayed quantum choice eraser (and so causing the interference pattern at $D_0$ to vanish.) Actually as I've described it, it would be even a message from the future.
Question If there would be interference pattern, what's wrong in the above faster-than-light communication protocol?
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