2020/12/31 by Marco A. Rodríguez-García, Isaac Pérez Castillo, Pablo Barberis-Blostein +1 · 9 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Estimation theory #Estimator #Mathematical optimization #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum computer #Quantum mechanics #Quantum metrology #Quantum network #Quantum state #Qubit #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.22331/q-2021-06-04-467
published in Quantum 5, 467 (Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften) · 22 pages, 6 figures and 1 table
arxiv created 2021/06/02 · openalex publication_date 2021/06/04 · arxiv updated 2021/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.