Weak value amplification and beyond the standard quantum limit in position measurements

TL;DR

This paper analyzes the effectiveness of weak value amplification in enhancing measurement sensitivity in quantum optics, concluding it does not surpass the standard quantum limit when quantum noise is properly considered.

Contribution

The study formulates weak value amplification within the Heisenberg picture and demonstrates it does not improve sensitivity beyond the standard quantum limit in optical interferometry.

Findings

Sensitivity limit equals the standard quantum limit.

Weak value amplification does not surpass fundamental quantum noise.

Discussion of methods to potentially beat the standard quantum limit.

Abstract

In a weak measurement with post-selection, a measurement value, called the weak value, can be amplified beyond the eigenvalues of the observable. However, there are some controversies whether the weak value amplification is practically useful or not in increasing sensitivity of the measurement in which fundamental quantum noise dominates. In this paper, we investigate the sensitivity limit of an optical interferometer by properly taking account quantum shot noise and radiation pressure noise. To do so, we formulate the weak value amplification in the Heisenberg picture, which enables us to intuitively understand what happens when the measurement outcome is post-selected and the weak value is amplified. As a result, we found that the sensitivity limit is given by the standard quantum limit that is the same as in a standard interferometry. We also discuss a way to circumvent the standard quantum limit.