Strong measurements give a better direct measurement of the quantum wave function

TL;DR

This paper demonstrates that strong measurements can directly measure the quantum wavefunction more accurately and precisely than weak measurements, challenging the traditional reliance on weak measurements for wavefunction reconstruction.

Contribution

It introduces a method for direct wavefunction measurement using measurements of arbitrary strength, showing strong measurements outperform weak ones in most cases.

Findings

Strong measurements outperform weak measurements in accuracy and precision.

Exact expression for the difference between reconstructed and original wavefunctions.

Defines the applicability range of weak measurement-based wavefunction reconstruction.

Abstract

Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wavefunction [Nature (London) 474, 188 (2011)]. Here we show that direct measurement of the wavefunction can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e. those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the reconstructed and original wavefunctions obtained by the weak measurement approach: this will allow to define the range of applicability of such method.