Puentes, Hermosa, and Torres Reply:

Abstract

In a preceding Comment [1] to our Letter [2] concerning weak measurements with orbital-angular-momentum (OAM) pointer states [2], Pan and Panigrahi show that the real and imaginary parts of higher-order weak values can be made accessible using Gaussian pointer states.In [2], our goal is to show that by using pointer states embedded with OAM it is possible to extract higher-order weak values where pointer states with a Gaussian shape cannot.As a consequence, our work put forward a new tool for weak amplification schemes, i.e., the use of pointer states with more general spatial forms that could be advantageous in some scenarios.We did not intend to claim that a pointer state with orbital angular momentum was needed to extract higherorder weak values in general.We clarify our point with this Reply.In our Letter we consider a specific Hamiltonian of interaction of the form H ¼ g A AP x þ g B BP y , where A, B are operators, (P x , P y ) are the pointer momentum operators, conjugate to the pointer position operators (X, Y), and g A;B are coupling constants.Moreover, we calculate the two-dimensional pointer displacement hXYi, corresponding to a specific measurement.We emphasize that we consider a particular interaction and a specific measurement, which are generally dictated by the physical system under investigation.The result, Eq. ( 4) of our Letter, shows that pointer states with OAM (l ¼ Æ1) can be used to retrieve the imaginary part of the higher-order weak values hA 2 i w and hB 2 i w , whereas this is not possible with pointer states with no OAM (l ¼ 0).In addition, Eq. ( 9) of our Letter shows, by means of a specific example with B ¼ 0, that hXYi ¼ 0 for Gaussian pointer states.On the contrary, a pointer state with l ¼ Æ1 allows us to extract the imaginary part of the weak value hA 2 i w .Pan and Panigrahi show that by measuring hX 2 i one can obtain the real part of the weak value hA 2 i w using a Gaussian pointer [see Eq. ( 4) of [1]].However, in order to access its imaginary part, they are forced to use a different interaction Hamiltonian, and a measurement observable involving noncommuting operators.The work of Pan and Panigrahi proves the strength of our proposal: One