Phase information transfer by post-selection in Spin--Mechanical assisted magnetometry

Abstract

Quantum information transfer between light-matter-type systems is poised to enable important applications, while also serving as a testbed for theoretical investigation. Such systems can be realized with spins coupled to a mechanical oscillator, a platform that has been extensively studied both theoretically and experimentally. Early demonstrations of quantum information transfer have relied mostly on coherent control. However, measurement-induced backaction has emerged as a strong alternative for quantum control. In this work we use post-selection on the spin system as a selective backaction to refocus spin's phase information onto the mechanical oscillator. We identify physical resources and operating regimes that govern conditional phase transfer, including oscillator quantum coherence, the number of spins, the mechanical initial state, coupling strength, oscillator amplitude, and relaxation. We benchmark different scenarios using the variance as the figure of merit, estimated via two complementary approaches: a semiclassical variance estimator and a Pegg-Barnett quantum estimator. The Cramér-Rao bound is also computed for comparison. The analysis provides a framework for understanding phase transfer in high-dimensional hybrid quantum systems and for measurement-induced backaction used in quantum magnetometry.