This was a poorly written article, in my opinion. It failed to communicate the intent of the paper. I think it's trying to say something like... In quantum inf

This was a poorly written article, in my opinion. It failed to communicate the intent of the paper. I think it's trying to say something like... In quantum information theory there's pure states, like "[Off]", "[On]", "([Off] + [On])/sqrt(2)", "([Off] - [On])/sqrt(2)", and "3/5 [Off] + 4i/5 [On]". There's also mixed states, which are probability distributions of pure states, like "35% [On] + 65% [Off]" or "10% [On] + 90% ([Off] + [On])/sqrt(2)". Pure states behave differently from mixed states (sometimes), which is why the distinction is worth having. Pure states collapse into mixed states when measured. There's a process to convert any mixed state into a pure state, called purification [1], that works by grafting on a secondary system with the appropriate entanglements. For example, "10% [On] + 90% ([Off] + [On])/sqrt(2)" can be purified into "sqrt(1/10) [On and Extra=0] + sqrt(9/20) [Off and Extra=1] + sqrt(9/20) [On and Extra=1]". This isn't just a theoretical trick to ignore mixed-ness, it's something you can do in practice. You can even verify that it works, statistically, because pure states interfere and correlate in ways that some mixed states can't. The article appears to be saying that any theory that allows for purification (however they define it) must secretly be isomorphic to quantum mechanics (i.e. the state space is tensor products of complex vectors, the operations are unitary matrices, and measurement outcomes are related to the eigenvalues/vectors of Hermitian matrices). 1: http://en.wikipedia.org/wiki/Purification_of_quantum_state http://en.wikipedia.org/wiki/Purification_of_quantum_state