Comment on "Weak Measurements with Orbital-Angular-Momentum Pointer states"

In a recent Letter (Phys. Rev. Lett. 109, 040401 (2012)), G. Puentes, N. Hermosa and J. P. Torres report a scheme for extracting higher-order weak values by using orbital-angular momentum states as pointer states. They claim that such weak values are inaccessible with a Gaussian pointer state only. In this Comment, we show that the Gaussian pointer state by itself can provide access to the higher-order weak value, if suitable pointer displacement is observed.