Frequency estimation under non-Markovian spatially correlated quantum noise: Restoring superclassical precision scaling

TL;DR

This paper investigates how entanglement-enhanced Ramsey interferometry can achieve super-classical precision scaling even under complex, non-Markovian, spatially correlated quantum noise, by analyzing the effects of probe configuration randomization.

Contribution

It provides an exact expression for the reduced density matrix under non-Markovian Gaussian dephasing and demonstrates how randomizing probe locations can restore super-classical scaling.

Findings

Randomizing probe locations can suppress spatial correlation effects.

Superclassical precision scaling is achievable with entangled states.

Analysis applies to spin-boson dephasing in thermal environments.

Abstract

We study the estimation precision attainable by entanglement-enhanced Ramsey interferometry in the presence of spatiotemporally correlated non-classical noise. Our analysis relies on an exact expression of the reduced density matrix of the qubit probes under general zero-mean Gaussian stationary dephasing, which is established through cumulant-expansion techniques and may be of independent interest in the context of non-Markovian open dynamics. By continuing and expanding our previous work [Beaudoin et al., Phys. Rev. A 98, 020102(R) (2018)], we analyze the effects of a non-collective coupling regime between the qubit probes and their environment, focusing on two limiting scenarios where the couplings may take only two or a continuum of possible values. In the paradigmatic case of spin-boson dephasing noise from a thermal environment, we find that it is possible to suppress, on average, the effect of spatial correlations by randomizing the location of the probes, as long as enough configurations are sampled where noise correlations are negative. As a result, superclassical precision scaling is asymptotically restored for initial entangled states, including experimentally accessible one-axis spin-squeezed states.