Is this double "double slit experiment" involving entanglement possible? The experiment goes as follows:
Put a particle emitter (photon, electron etc.) between a pair of double slits. The emitter launches pairs of particles that are entangled in such a way that if one goes through slit A the other goes through slit 2, if one goes through slit B the other goes through slit 1. 

My prediction for this experiment is that if we put a detector on slit A (or any other slit) that can detect through which slit one of the particles went through then no interference patter will form on ether side of the emitter, if we don't place a detector 
we should see interference patterns emerge on both sides.
Is this experiment possible?
If so, was this or an equivalent experiment ever done? 
 A: There is no reason in principle, that I can think of, for this experiment to be impossible. The entanglement could be achieved by aligning the source and the slits so that the upper slit on one side, the source and the lower slit on the other side are in a line. If the particles are produced in pairs with no total momentum then they will be emitted in opposite directions, so if one goes through the upper slit, the other must go through the lower slit. 
I doubt this set up has ever been tested, but equivalent experiments have been done using entangled electron. In these electron experiments the roles of "goes through the upper/lower slit" is played by the electron's spin being up or down in some particular direction. It terns out that measurements of the electrons spin in a direction at $90^\circ$ to your chosen direction can be understood in terms of interference between the spin up and spin down states. 
In terms of the result of the experiment I don't think you will observe interference in either case. An intuitive way to see that this has to be true is to imagine we set up the two slits a light year apart and the source sends a pair of pulses containing a large number of entangled photons. If I am waiting at one screen I can wait until just before the photons arrive to decide whether or not to measure which slit they pass through. If you are waiting at the other screen then if the result you observe depends on whether I measured my photons or not, then we could use this to send a message faster than light. Since we can't do that and since if I measure my photon then we know which slit yours went through, it must be that you never observe an interference pattern.
This isn't as weird as it first seems (at least once you are used to the regular double slit experiment anyway) Effectively all we have done is measure which slit the photon passes through when it is first created, by creating its entangled partner, rather than doing it when the photon actually passes through the slits. 
A: Looks like someone actually did a version of this experiment and you can get an interference pattern on both screens if and only if you don't measure which slit either photon passes through.
I found very interesting that removing one of the screens and letting one photon pass though and propagate indefinitely through space means no interference pattern will be present on the remaining screen.
