  We demonstrate the role of measurement back-action of a coherent spin
environment on the dynamics of a spin (qubit) coupled to it, by inducing
non-classical (Quantum Random Walk like) statistics on its measurement
trajectory. We show how the long-life time of the spin-bath allows it to
correlate measurements of the qubit over many repetitions. We have used
Nitrogen Vacancy centers in diamond as a model system, and the projective
single-shot readout of the electron spin at low temperatures to simulate these
effects. We show that the proposed theoretical model, explains the
experimentally observed statistics and their application for quantum state
engineering of spin ensembles towards desired states.
