Experimental realization of post-selected weak measurements on an NMR quantum processor

Abstract

The ability to post-select the outcomes of an experiment is a useful\ntheoretical concept and experimental tool. In the context of weak measurements\npost-selection can lead to surprising results such as complex weak values\noutside the range of eigenvalues. Usually post-selection is realized by a\nprojective measurement, which is hard to implement in ensemble systems such as\nNMR. We demonstrate the first experiment of a weak measurement with\npost-selection on an NMR quantum information processor. Our setup is used for\nmeasuring complex weak values and weak values outside the range of eigenvalues.\nThe scheme for overcoming the problem of post-selection in an ensemble quantum\ncomputer is general and can be applied to any circuit-based implementation.\nThis experiment paves the way for studying and exploiting post-selection and\nweak measurements in systems where projective measurements are hard to realize\nexperimentally.\n