Weak values and the quantum phase space

TL;DR

This paper explores the concept of weak values in quantum mechanics within the phase space framework, emphasizing the importance of measurement effects and proposing a symmetric approach suitable for quantum optics.

Contribution

It extends previous work by incorporating phase space effects and using coherent states to improve the understanding of weak measurements in quantum systems.

Findings

Measurement results can be symmetric in position and momentum

Phase space considerations are crucial for accurate weak value analysis

Proposes a quantum optical implementation approach

Abstract

We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring process on the entire phase space of the measuring system. By using coherent states, we go a step further than Jozsa in a recent paper, and we present an example where the result of the measurement is symmetrical in the position and momentum observables and seems to be much better suited for quantum optical implementation.