Precision metrology of weak measurement with thermal state pointer

TL;DR

This paper investigates the advantages of using thermal state pointers in weak quantum measurements, demonstrating enhanced measurement precision and Heisenberg-limited scaling, which outperform pure state pointers and are easier to implement.

Contribution

It reveals that thermal states can improve weak measurement precision and achieve Heisenberg limit scaling, offering practical benefits over pure or coherent states.

Findings

Maximal QFI with thermal pointer reaches thermal fluctuation level.

Thermal states enable Heisenberg limit in Kerr nonlinear systems.

Thermal states' large uncertainty is easily achievable and beneficial.

Abstract

Quantum metrology is being gradually studied for weak measurement systems. For weak measurement systems with thermal state pointer, we find that in the displacement space corresponding to imaginary weak values, the maximal QFI after successful postselection can attain the level of thermal fluctuations, without surpassing total QFI, and that QFI which increases with increasing temperature can constantly improve the measurement precision. These results are much better than that of weak measurement with pure state (i.e., Gaussian state) pointer. On the other hand, in Kerr nonlinear interaction systems with weak measurement, and by using thermal state pointer, we obtain in the phase space successful postselection and postselected measurements both achieve the Heisenberg limit of quantum metrology, and show weak measurement with thermal states only obtain classical Fisher information (CFI) which increases with increasing temperature and achieves classical enhanced scaling of N^2. Moreover, weak measurement with thermal states has an advantage over that with coherent states or mixed states of the light because generating these states with more large uncertainty are limited under the current technology, but thermal states with more large uncertainly are very easy to achieve with increasing temperature in nature, regardless of thermal states of the light or the matter.