Quantum Metrology Assisted with Abstention

TL;DR

This paper demonstrates that allowing for abstention, or inconclusive results, can significantly enhance the precision of quantum phase estimation, providing analytical tools for understanding the trade-offs involved.

Contribution

It introduces a framework for incorporating abstention in quantum metrology, specifically in phase estimation, and derives analytical results for asymptotic behavior.

Findings

Abstention can drastically improve measurement precision.

Analytical tools for asymptotic behavior of precision and abstention rate.

Quantification of abstention needed for desired accuracy.

Abstract

The main goal of quantum metrology is to obtain accurate values of physical parameters using quantum probes. In this context, we show that abstention, i.e., the possibility of getting an inconclusive answer at readout, can drastically improve the measurement precision. We focus on phase estimation and quantify the required amount of abstention for a given precision. We also develop analytical tools to obtain the asymptotic behavior of the precision and required rate of abstention for arbitrary pure qubit states.