A generalized Arthurs-Kelly protocol for the simultaneous weak measurement of non-commuting observables.

In contrast to a projective quantum measurement, in a weak measurement, the system is only weakly perturbed while only partial information on the measured observable is obtained. During this talk, I will present a protocol for the simultaneous measurement of position and momentum of a quantum system that generalizes the Arthurs and Kelly (AK) approach. Starting with the AK protocol, a systematic extension to a corresponding weak measurement can be obtained along two steps: First, we introduce a Kraus operator that generalizes the transformation of quantum states of a system and detectors during the AK protocol, and demonstrate that this operator constitutes a positive operator valued measure (POVM) in the Hilbert space. Then, we identify the initial detector wavefunctions and the nature of the system-detector interaction that physically reproduces this mathematical construct, providing a complete physical picture for the realization of such weak measurements. Finally, I will compare our approach with alternative protocols recently suggested in the literature. We believe that the results of these investigations provide new insights that will help on the development of quantum control and quantum feedback technologies.