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A Logic of Quantum Measurement

Abstract : We present a formulation of quantum mechanics based on a logic representing some aspects of the behaviour of the measurement process. With such an approach, we make no direct mention of quantum states, and thus avoid the problems associated to this rather evasive notion. We then study some properties of the models of this logic, and deduce some characteristics that any model (and hence any formulation of quantum mechanics compatible with its prediction and relying on a notion of measurement) should verify. The main results we obtain are that in the case of a Hilbert space of dimension at least 3, no model can lead to the prediction with certainty of more than one atomic outcome. Moreover, if the Hilbert space is finite dimensional, then we are able to precisely describe the structure of the predictions of any model of our logic. As a consequence, we finally show that all the models of our logic make exactly the same predictions regarding whether a given sequence of outcomes is possible or not.
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https://hal.inria.fr/hal-01117527
Contributor : Olivier Brunet <>
Submitted on : Tuesday, February 17, 2015 - 11:47:31 AM
Last modification on : Friday, November 6, 2020 - 4:15:55 AM
Long-term archiving on: : Monday, May 18, 2015 - 10:20:41 AM

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  • HAL Id : hal-01117527, version 1
  • ARXIV : 1502.06759

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Olivier Brunet. A Logic of Quantum Measurement. 2015. ⟨hal-01117527⟩

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