Quantum metrology in the presence of spatially correlated noise: Restoring Heisenberg scaling

TL;DR

This paper investigates how spatially correlated noise affects quantum metrology, demonstrating that certain entangled states can maintain Heisenberg scaling despite environmental decoherence, highlighting the importance of noise correlations.

Contribution

It introduces analysis of finite correlation length noise, showing robust entangled states can preserve Heisenberg scaling under realistic noise conditions.

Findings

Robust entangled states maintain Heisenberg scaling with spatially correlated noise.

Spatial correlations in noise can protect quantum advantage in metrology.

Decoherence free subspaces are relevant even with finite correlation length.

Abstract

Environmental noise can hinder the metrological capabilities of entangled states. While the use of entanglement allows for Heisenberg-limited resolution, the largest permitted by quantum mechanics, deviations from strictly unitary dynamics quickly restore the standard scaling dictated by the central limit theorem. Product and maximally entangled states become asymptotically equivalent when the noisy evolution is both local and strictly Markovian. However, temporal correlations in the noise have been shown to lift this equivalence while fully (spatially) correlated noise allows for the identification of decoherence free subspaces. Here we analyze precision limits in the presence of noise with finite correlation length and show that there exist robust entangled state preparations which display persistent Heisenberg scaling despite the environmental decoherence, even for small correlation length. Our results emphasize the relevance of noise correlations in the study of quantum advantage and could be relevant beyond metrological applications.