Quantum Measurements from a Logical Point of View

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We present a formal logic modeling some aspects of the behavior of the quantum measurement process, and study some properties of the models of this logic, from which we deduce some characteristics that any such model should verify. In the case of a Hilbert space of dimension at least 3, we then show that no model can lead to the prediction with certainty of more than one atomic outcome. Moreover, if the Hilbert space is finite dimensional, we can precisely describe the structure of the predictions of any model of our logic. As a consequence, we also prove that all the models of our logic make exactly the same predictions regarding whether a given sequence of outcomes is possible.