Complex weak values in quantum measurement

In the weak value formalism of Aharonov et al., the 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.