Weak Value, Quasiprobability and Bohmian Mechanics

TL;DR

This paper explores the role of quasiprobability and weak values in quantum mechanics, demonstrating their connection to Bohmian mechanics and highlighting their significance in understanding noncommuting observables and contextuality.

Contribution

It clarifies the significance of quasiprobability in quantum mechanics and embeds it within Bohmian mechanics, revealing new insights into contextuality and the interpretation of quantum phenomena.

Findings

Quasiprobability allows consistent treatment of noncommuting observables.

Bohmian mechanics can be viewed as an ontological model with contextuality.

Weak value and quasiprobability clarify the connection between classical and quantum descriptions.

Abstract

We clarify the significance of quasiprobability (QP) 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.