Efficient qubit phase estimation using adaptive measurements

TL;DR

This paper introduces an adaptive measurement scheme for qubit phase estimation that surpasses traditional methods by approaching the quantum Cramér-Rao bound, demonstrated through simulations.

Contribution

The paper proposes a new adaptive measurement strategy using covariant measurements to improve qubit phase estimation accuracy beyond existing methods.

Findings

The proposed method approaches the quantum Cramér-Rao bound.

Monte Carlo simulations confirm the method's efficiency.

The scheme is more realistic and effective than current techniques.

Abstract

Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is given by the so-called quantum Cram\'er-Rao bound, so any measurement strategy aims to obtain estimations as close as possible to it. However, more often than not, the current state-of-the-art methods to estimate quantum phases fail to reach this bound as they rely on maximum likelihood estimators of non-identifiable likelihood functions. In this work we thoroughly review various schemes for estimating the phase of a qubit, identifying the underlying problem which prohibits these methods to reach the quantum Cram\'er-Rao bound, and propose a new adaptive scheme based on covariant measurements to circumvent this problem. Our findings are carefully checked by Monte Carlo simulations, showing that the method we propose is both mathematically and experimentally more realistic and more efficient than the methods currently available.