A No-Go Theorem For Theories That Decohere To Quantum Mechanics

Quantum theory is the most accurately tested theory of Nature in the history of science. Yet it may be the case that quantum theory is only an effective description of our world, in the same way that classical physics is an effective description of the quantum world. This work asks whether there exists an operationally-defined theory that supersedes quantum theory, but that reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification. Causality formalises the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. In a sense, purification can be thought of as a statement of ``information conservation''; any missing information about the state of a given system can always be accounted for by considering it as part of a larger system. Hence, our result can either be viewed as evidence that the fundamental theory of Nature is quantum, or as highlighting the ways a post-quantum theory must radically depart from a quantum description of the world.