> Axiom 5 (which requires that there exist continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or eve

> Axiom 5 (which requires that there exist continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or even just the word "continuous" from Axiom 5) is dropped then we obtain classical probability theory instead. I actually recently read this paper and wondered the following question: what experiment supports the need for axiom 5, distinguishing quantum mechanics from classical probability theory? This came up because I always hear about "2-norm preserving unitary operators" as the only reasonable theory for quantum computing, which is of course different from classical probability. Is it just Occam's razor that to achieve the same results in experiments one would need to impose some large number of new states to a particle? Most of my understanding comes from a light reading of Nielsen-Chuang and Aaronson's stuff. (A minor tangent: a theorem from computer science informs me that complex numbers aren't needed if you're willing to get a "good enough approximation" and polynomial blowup, but this paper argues complex numbers are necessary, even for finite/countable state spaces; I want to read the paper a bit closer to figure out where this discrepancy is). This culminated in the following physics stackexchange question, which was probably not worded in the best way for the physics community[1]. I still don't really understand any of the answers. Maybe someone on HN can elucidate it for me :) [1]: http://physics.stackexchange.com/questions/205742/what-experiment-supports-the-axiom-that-quantum-operations-are-reversible http://physics.stackexchange.com/questions/205742/what-exper...