Reference-frame-independent quantum metrology

TL;DR

This paper introduces methods for nonlinear quantum metrology without a shared reference frame, utilizing local measurements and invariants to achieve precision scaling even under decoherence.

Contribution

It develops systematic techniques for reference-frame-independent quantum metrology, including analytical precision formulas and analysis under decoherence.

Findings

Derived metrological precision using local invariants.

Provided analytical expressions for precision scaling in nonlinear scenarios.

Analyzed the impact of local decoherence on measurement precision.

Abstract

How can we perform a metrological task if only limited control over a quantum system is given? Here, we present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. Our approach involves preparing multiple copies of quantum systems and then performing local measurements with randomized observables. First, we derive the metrological precision using an error propagation formula based solely on local unitary invariants, which are independent of the chosen basis. Next, we provide analytical expressions for the precision scaling in various examples of nonlinear metrology involving two-body interactions, like the one-axis twisting Hamiltonian. Finally, we analyze our results in the context of local decoherence and discuss its influences on the observed scaling.