Weak Value, Quasiprobability and Bohmian Mechanics

Foundations of Physics 47 (2):236-255 (2017)
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Abstract

We clarify the significance of quasiprobability in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov’s weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality.

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References found in this work

The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.
Can the ontological models framework accommodate Bohmian mechanics?Benjamin Feintzeig - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 48 (1):59-67.

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