After a big discussion on this topic on madisound forum, samples were sent out and 4 people could not hear a difference (including speaker designer Dennis Murphy) while one person could hear slight differences and one person being totally convinced. A lot of people on audioasylum seem to like the Bybees.
So much for empirical evidence. As for the theory behind it, the detailed technology behind bybee is classified information. Insert whatever cynical remark here.
The superficial technical explanations on the bybee website pertaining quantum noise and the regulation thereof are very entertaining but hold little value. "Quantum noise energy is stripped off the electrons [which then dissipates as heat] or "increasing signal velocity" just give two examples.
The old ads claimed that the quantum purifier also cures impedance mismatches. I wonder how, being non-reactive and having no impedance to speak of.
The older Bybees were also a potential fire hazard.
But hey, if it works, that's cool. Companies like Modwright and Boldercables are convinced of Bybees. But even if there is a difference, I doubt the price will hardly meet the benefit - juding by the mixed reports and the high price. I simply have neither the wit nor the money to try out all the dubious tweaks in existence, and the Bybee ranks very high up there along with the clever clock and rainbow foil in the "most dubious" - category.