According to Reichenbach's criterion, correlations may come through two structures: common cause, or direct causation. For the case of correlations obtained by measuring entangled systems, Bell famously excluded any explanation relying only on a common cause. A few years ago, we first intuited [1,2] and then finally proved [3,4] that direct causation can also be excluded up to the extreme case of influences with infinite speed in a preferred frame (or similar, more complex variations [5]). More precisely, if quantum correlations were due to influence at finite (albeit superluminal) speed, then it would be possible even for observers to communicate faster than light. The argument uses three or more particles. I shall review these ideas, with the hope that some could be tested in a proof-of-principle experiment.
[1] VS, N. Gisin, Phys. Lett. A 295, 167 (2002) //arxiv.org/abs/quant-ph/0110074
[2] VS, N. Gisin, Braz. J. Phys. 35, 328 (2005) (Proceedings of DICE 2004) //arxiv.org/abs/quant-ph/0410025
[3] J.D. Bancal et al., Nature Physics 8, 867 (2012) //arxiv.org/abs/1110.3795
[4] T. Barnea et al. Phys. Rev. A 88, 022123 (2013) //arxiv.org/abs/1304.1812
[5] VS et al., Found. Phys. 44, 523-531 (2014) //arxiv.org/abs/1304.0532
