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

Abstract

In this work, the measurement transition as well as precision measurement advantages of singlephoton-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 ratios 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.

General approach of weak-to-strong measurement transition for Fock-state-based pointer states

“…( 45) and Eq. ( 46) are confirmed in many related studies [30,32,33], and holds for any pointer states.…”

“…One of the interesting points in von Neumann measurement model is that the coupling strength between the measured system and pointer can take arbitrary value so that we can connect the weak and strong measurements by adjusting it. Recently, the weak-to-strong measurement transition problems are investigated experimentally [31] and theoretically [32,33] for some specific pointer states. However, the general approach of weak-to-strong measurement transition applicable for arbitrary pointers has not been studied yet.…”