arXiv:1208.4123quant-ph
The completeness of quantum theory for predicting measurement outcomes
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Abstract
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that provide improved predictions. Here we review recent work that considers arbitrary alternative theories, constrained only by the requirement that they are compatible with a notion of "free choice" (defined with respect to a natural causal order). It is shown that quantum theory is "maximally informative", i.e., there is no other compatible theory that gives improved predictions. Furthermore, any alternative maximally informative theory is necessarily equivalent to quantum theory. This means that the state a system has in such a theory is in one-to-one correspondence with its quantum-mechanical state (the wave function). In this sense, quantum theory is complete.
There is lots of mathematical evidence that every quantum state maps 1-to-1 on a physical state¹, or at least be uniquely determined by the physical state². The main assumption both make is that there is some physical state. So it doesn't really matter if it's a map or not - it…
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