Efficient qubit phase estimation using adaptive measurements

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 Cramér-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 Cramér-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.

arXiv comment22 pages, 6 figures and 1 table

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Cited by in corpus (6)

• Benchmarking Machine Learning Algorithms for Adaptive Quantum Phase Estimation with Noisy Intermediate-Scale Quantum Sensors
• Determination of the asymptotic limits of adaptive photon counting measurements for coherent-state optical phase estimation
• Measuring quantum relative entropy with finite-size effect
• Towards Practical Quantum Phase Estimation: A Modular, Scalable, and Adaptive Approach
• Usefulness of Quantum Entanglement for Enhancing Precision in Frequency Estimation
• Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution