Superresolution in Quantum Noise Spectroscopy via Filter Design

TL;DR

This paper develops a quantum control framework using filter functions to achieve superresolution in quantum noise spectroscopy, enabling discrimination of closely spaced spectral lines beyond traditional limits.

Contribution

It introduces analytic conditions and an optimal control approach for superresolution, extending to entangled states and practical quantum sensing platforms.

Findings

Derived general conditions for superresolution using filter functions

Developed an optimal control framework for superresolution protocols

Demonstrated potential advantages of entangled states in resolution

Abstract

Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate between spectral lines with arbitrarily small frequency separation. Here, we revisit this problem from the perspective of quantum control theory, utilizing the filter function formalism to derive general, analytic conditions on quantum control protocols for achieving superresolution. Building on these conditions, we develop an optimal control framework, the utility of which is demonstrated through numerical identification of superresolution control protocols in the presence of realistic, experimentally-relevant constraints. We further extend our results to entangled initial states and assess their potential advantage. Our approach is broadly applicable to a wide variety of quantum sensing platforms, and it provides a systematic path to discover novel protocols that surpass conventional resolution limits in these systems.