Making the most of time in quantum metrology: concurrent state preparation and sensing

TL;DR

This paper investigates how to optimize quantum metrology protocols by considering non-negligible state preparation and readout times, demonstrating that concurrent twisting and sensing can improve sensitivity under limited time resources.

Contribution

It introduces a framework for including preparation and readout times in quantum sensing, showing benefits of concurrent operations and extending results to optical systems.

Findings

Entanglement via twisting offers no advantage unless time or twisting strength is sufficient.

Concurrent application of twisting and sensing enhances resource utilization.

Results are extended to optical regimes using Holstein-Primakoff transformation.

Abstract

A quantum metrology protocol for parameter estimation is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. In the present work we consider non-negligible state preparation and readout times, and the tradeoffs in sensitivity that come when a limited time resource $\tau$ must be divided between the three stages. To investigate this, we focus on the problem of magnetic field sensing with spins in one-axis twisted or two-axis twisted states. We find that (accounting for the time necessary to prepare a twisted state) by including entanglement, which is introduced via the twisting, no advantage is gained unless the time $\tau$ is sufficiently long or the twisting sufficiently strong. However, we also find that the limited time resource is used more effectively if we allow the twisting and the magnetic field to be applied concurrently which is representative of a more realistic sensing scenario. We extend this result into the optical regime by utilizing the exact correspondence between a spin system and a bosonic field mode as given by the Holstein-Primakoff transformation.