Lossless Postselected Quantum Metrology with Quasi-pure Mixed States

TL;DR

This paper generalizes lossless postselected quantum metrology from pure to quasi-pure mixed states, enabling improved sensitivity in noisy environments through classical correlations and broadening applications in quantum imaging and estimation.

Contribution

It introduces a theory for lossless postselection of quasi-pure mixed states, extending quantum metrology techniques to decoherence-affected scenarios.

Findings

Quasi-pure states can be engineered via classical correlations with an ancilla.

The approach enhances quantum imaging and unitary estimation under noise.

The method broadens the applicability of postselection in quantum metrology.

Abstract

Postselection can compress the metrological information and improve sensitivity in the presence of certain types of technical noise. Postselected quantum metrology with pure states has been significantly advanced recently. However, extending this framework to mixed states leads to formidable challenges, such as the difficulty in searching for lossless postselection measurements or even the loss of metrological information. In this work, we leverage the intuition for the lossless postselection of pure states and generalize the theory to the lossless postselection of a class of mixed states, dubbed quasi-pure states. We illustrate our findings in postselected quantum imaging, unitary estimation problems, and show that the quasi-pure structure can be universally engineered through only classical correlation with an ancilla. Our findings extend the utility of postselection techniques to scenarios with decoherence and also offer new perspectives to foundational questions in quantum information geometry.