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You can't test if quantum uses complex numbers
Craig Gidney's computer science blog
What Renou et al are actually claiming is that if you start with quantum mechanics, and then remove all operations and states involving non-real numbers, and then try to emulate what was lost using what remains, you will fail in an experimentally detectable way. But this solution doesn’t translate back to the physics use case that Renou et al have in mind, where basically the whole universe isn’t trusted, so I’m not going to allow it. “Quantum theory based on real numbers can be experimentally falsified, unless entanglement is present, which it easily could be, and we have no way of testing that it isn’t”; it flows right off the tongue.
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