I've just seen yet another reason to issue the reminder that, whatever a quantum superposition is, we shouldn't really be saying that the system is "in two states at once."
States and observables are two sides of the same coin. To affirm the coherence of a quantum superposition of two states is to affirm the measurability of observables capable of distinguishing that superposition from an incoherent one ascribing the same probabilities to each.
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This is the realization that lead Giancarlo Wick to formulate his superselection rules. You can add two eigenstates of the electric charge observable with different eigenvalues. But you can't measure any observable that distinguishes the result from an incoherent superposition.
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So if you want to affirm that every state formed by adding two other states is a coherent superposition, you must posit that every self-adjoint operator is observable. But this last assertion is known to be false (for, e.g., the electric charge observable.) So care is required.
End of conversation
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