Continuing the discussion from The Pilot Wave Interpretation of Quantum Mechanics:
One way we might see a violation of Bohm’s rule in quantum mechanics, a triple slit experiment:
The triple slit experiment uses three small openings instead of two. While it seems like a trivial change, if done correctly it allows for secondary interactions that could in principle violate the Born rule. Basically, if you just square the total wavefunction of the three slits, you get one probability distribution. If you calculate the secondary interactions you get a different distribution. The difference is extremely small, but in 2010 the experiment was performed, and found the Born rule held within experimental limits.
While this would seem to confirm the Born rule, the precision of the experiment was only to 1 part in 100, which isn’t very high. Unfortunately, even getting that level of precision is difficult with the triple-slit experiment.
The Experimental Quest To Disprove A Quantum Postulate