Complex weak values in quantum measurement

TL;DR

This paper provides a physical interpretation of complex weak values in quantum measurement, linking the real and imaginary parts to measurable shifts in the pointer’s position and momentum during weak measurements.

Contribution

It derives a novel physical interpretation of complex weak values, connecting them to observable shifts in measurement pointer variables.

Findings

Mean position shift relates to the imaginary part of the weak value.

Pointer spreading rate influences the measurement outcome.

Provides a clearer understanding of weak measurement dynamics.

Abstract

In the weak measurement formalism of Y. Aharonov et al. the so-called weak value A_w of any observable A is generally a complex number. We derive a physical interpretation of its value in terms of the shift in the measurement pointer's mean position and mean momentum. In particular we show that the mean position shift contains a term jointly proportional to the imaginary part of the weak value and the rate at which the pointer is spreading in space as it enters the measurement interaction.