Optimal Probe Wavefunction of Weak-Value Amplification

TL;DR

This paper derives the optimal probe wavefunction for weak-value amplification, showing that the amplification factor can be unbounded and the amplified signal remains sharp, improving measurement sensitivity.

Contribution

The authors explicitly determine the optimal probe wavefunction and amplification factor for weak measurements, revealing unbounded amplification potential beyond Gaussian probes.

Findings

Amplification factor has no upper bound.

Optimal probe wavefunction maximizes signal amplification.

Amplified signal remains sharp despite large amplification.

Abstract

The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is larger for the post-selected state more orthogonal to the initial state. Recently, the signal amplification by the weak measurement has been extensively studied. In the present work, we explicitly obtain the optimal probe wavefunction and the amplification factor for a given weak value, which is calculated from the experimental setup. It is shown that the amplification factor has no upper bound in contrast to the Gaussian probe wavefunction and that the amplified signal is sharp.