Using Weak Measurements to Synthesize Projective Measurement of Nonconserved Observables of Weakly Coupled Nuclear Spins

Abstract

Projective quantum measurement is fundamental for quantum technologies. Here we propose a method for construction of projective measurement of nonconserved quantity of nuclear spin via a weakly coupled auxiliary electron spin. The key idea is to apply suitable quantum control on the electron to construct a weak quantum nondemolition (QND) measurement on the nuclear spin and then cascade a sequence of such measurements into a projective one. We identify a set of tunable parameters to select the QND observables and control the strength of the weak QND measurement. We also find that the QND measurement can be stabilized against realistic experimental control errors. As a demonstration of our method, we design projective measurement on a ${}^{13}\mathrm{C}$ nuclear spin weakly coupled to a nitrogen-vacancy center electron spin in diamond.