Single-photon-added coherent state based measurement transition and its advantages in precision measurement

TL;DR

This paper investigates how single-photon-added coherent states can enhance measurement precision through postselected von Neumann measurements, revealing the transition from weak to strong measurement and analyzing the impact on signal-to-noise ratio and quantum Fisher information.

Contribution

It introduces the use of single-photon-added coherent states in measurement transition analysis and demonstrates their advantages in improving precision in quantum measurements.

Findings

Single-photon-added coherent states improve signal-to-noise ratio.

Postselection enhances quantum Fisher information.

Large weak values do not necessarily improve measurement precision.

Abstract

In this work, the measurement transition as well as precision measurement advantages of single-photon-added coherent state after postselected von Neumann measurement are investigated. We noticed that the weak-to-strong measurement transition characterized by the shifts of pointer's position and momentum variables occurred in continuously by controlling a dimensionless parameter associated with system-pointer coupling. We calculate the ratio between the signal-to-noise ratio of nonpostselected and postselected measurements, and the latter is used to find the quantum Fisher information. We found that the single-photon-added coherent pointer state can improve the precision of the measurement processes such as signal-to-noise ratio and parameter estimation after postselected von Neumann measurement characterized by postselection and weak value. Furthermore, contrary to the results of several previous studies, we found that the anomalous large weak values can't improve the precision measurement processes related to single-photon-added coherent state.