Bell Experiments with Random Destination Sources

It is generally assumed that sources sending randomly two particles to one or two different observers, named here random destination sources (RDS), cannot by used for genuine quantum nonlocality tests because of the postselection loophole. We demonstrate that Bell experiments not affected by the postselection loophole may be performed with: (i) RDS and local postselection using perfect detectors, (ii) RDS, local postselection, and fair sampling assumption with any detection efficiency, and (iii) RDS and a threshold detection efficiency required to avoid the detection loophole. These results allow the adoption of RDS setups, which are more simple and efficient, for long-distance free-space Bell tests, and extends the range of physical systems which can be used for loophole-free Bell tests.