Actually, despite the title, the claim in the paper is that real-only-QM could be falsified, not that it has been. As far as I can tell, no one has actually do

Actually, despite the title, the claim in the paper is that real-only-QM could be falsified, not that it has been. As far as I can tell, no one has actually done the experiment to check. Logically, it's just as possible that complex-QM could fall. There's a certain amount of hubris in seeing a case where there are two theories that agree in all known cases except one we haven't checked, and assuming "Well that must mean the one we thought of first is right!"