Precision limit under weak-coupling with ancillary qubit

TL;DR

This paper introduces a quantum metrology protocol using a probe-ancilla system with weak coupling, achieving near-Heisenberg limit precision through optimized measurement strategies, even with imperfections.

Contribution

It presents a novel measurement-based quantum metrology method utilizing weak probe-ancilla interactions to attain quadratic scaling in precision, surpassing standard quantum limits.

Findings

Quadratic scaling of quantum Fisher information with probe size

Phase sensitivity approaches the Heisenberg limit

Protocol is robust against encoding and coupling imperfections

Abstract

We propose a measurement-based quantum metrology protocol in a composite model, where the probe system (a spin ensemble) is coupled to an ancillary two-level system (qubit) with a general Heisenberg XXZ interaction. With an optimized and weak probe-ancilla coupling strength and a proper duration of joint evolution, the two parallel evolution paths of the probe system induced by the unconditional measurement on qubit can transform an eigenstate of the collective angular momentum operator of spin ensemble to be a two-component state with a large distance in eigenspace. The quantum Fisher information about the phase encoded in the probe system of polarized states or their superposition, that could be relaxed to mixed states, can therefore manifest an exact or asymptotic quadratic scaling with respect to the probe size (spin number) $N$. The quadratic scaling behavior is found to be insensitive to the imperfect encoding operator and coupling strength. By virtue of the parity detection on the ancillary qubit or the probe system, the phase sensitivity can approach the Heisenberg limit. We suggest that the unconditional measurement on qubit could become an efficient resource to replace Greenberger-Horne-Zeilinger-like states and squeezing Hamiltonian for exceeding the standard quantum limit in metrology precision.