Quantum metrology with mixed states: When recovering lost information is better than never losing it

TL;DR

This paper explores how mixed quantum states, when properly purified and measured with auxiliary systems, can achieve near-Heisenberg-limited precision in quantum metrology, offering practical advantages over pure states.

Contribution

It introduces a method to design mixed states with purifications that serve as excellent metrological resources, including optimal measurement strategies to reach theoretical sensitivity limits.

Findings

Mixed states can achieve near-Heisenberg-limited metrology.

Purifications of mixed states can be optimized for quantum sensing.

Optimal measurement procedures saturate the quantum Cramér-Rao bound.

Abstract

Quantum-enhanced metrology can be achieved by entangling a probe with an auxiliary system, passing the probe through an interferometer, and subsequently making measurements on both the probe and auxiliary system. Conceptually, this corresponds to performing metrology with the purification of a (mixed) probe state. We demonstrate via the quantum Fisher information how to design mixed states whose purifications are an excellent metrological resource. In particular, we give examples of mixed states with purifications that allow (near) Heisenberg-limited metrology, and provide example entangling Hamiltonians that can generate these states. Finally, we present the optimal measurement and parameter-estimation procedure required to realize these sensitivities (i.e. that saturate the quantum Cram\'er-Rao bound). Since pure states of comparable metrological usefulness are typically challenging to generate, it may prove easier to use this approach of entanglement and measurement of an auxiliary system. An example where this may be the case is atom interferometry, where entanglement with optical systems is potentially easier to engineer than the atomic interactions required to produce nonclassical atomic states.