Quantum measurements with preselection and postselection

TL;DR

This paper analyzes quantum measurement processes involving preselection and postselection, deriving exact results for measurement outcomes across all coupling strengths, and explores how weak measurements can amplify signals but face limitations due to postselection probabilities.

Contribution

It provides exact expressions for measurement results without coupling restrictions and investigates the limits of signal amplification and sensitivity enhancement in quantum measurements.

Findings

Weak interactions can significantly amplify measurement signals.

Strong interactions reproduce ideal quantum measurement results.

Signal-to-noise ratio and measurement sensitivity improvements are limited by postselection probabilities.

Abstract

We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-tonoise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.