Advantages of nonclassical pointer states in postselected weak measurements

TL;DR

This paper demonstrates that non-classical pointer states, such as squeezed vacuum and Schrödinger cat states, enhance the precision of postselected weak measurements compared to semi-classical states, across various interaction strengths.

Contribution

It introduces the use of non-classical pointer states in weak measurement theory and shows their superiority over semi-classical states in measurement precision.

Findings

Non-classical pointer states improve signal-to-noise ratio.

Postselected weak measurements with non-classical states outperform semi-classical states.

Quantum Fisher information is higher with non-classical pointer states.

Abstract

We investigate, within the weak measurement theory, the advantages of non-classical pointer states over semi-classical ones for coherent, squeezed vacuum, and Schr\"{o}inger cat states. These states are utilized as pointer state for the system operator $\hat{A}$ with property $\hat{A}^{2}=\hat{I}$, where $\hat{I}$ represents the identity operator. We calculate the ratio between the signal-to-noise ratio (SNR) of non-postselected and postselected weak measurements. The latter is used to find the quantum Fisher information for the above pointer states. The average shifts for those pointer states with arbitrary interaction strength are investigated in detail. One key result is that we find the postselected weak measurement scheme for non-classical pointer states to be superior to semi-classical ones. This can improve the precision of measurement process.