  A weak measurement on a system is made by coupling a pointer weakly to the
system and then measuring the position of the pointer. If the initial
wavefunction for the pointer is real, the mean displacement of the pointer is
proportional to the so-called weak value of the observable being measured. This
gives an intuitively direct way of understanding weak measurement. However, if
the initial pointer wavefunction takes complex values, the relationship between
pointer displacement and weak value is not quite so simple, as pointed out
recently by R. Jozsa. This is even more striking in the case of sequential weak
measurements. These are carried out by coupling several pointers at different
stages of evolution of the system, and the relationship between the products of
the measured pointer positions and the sequential weak values can become
extremely complicated for an arbitrary initial pointer wavefunction.
Surprisingly, all this complication vanishes when one calculates the cumulants
of pointer positions. These are directly proportional to the cumulants of
sequential weak values. This suggests that cumulants have a fundamental
physical significance for weak measurement.
