Quantum phase estimation with a general binary-outcome measurement

• Published in: Results in physics Vol. 43; p. 106051
• Main Authors: Zheng, H.L., Ren, X.J., Liu, P., Jin, G.R.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-12-2022; Elsevier
• Subjects: Binary-outcome measurement; Mach–Zehnder interferometer; Quantum metrology; Quantum standard limit; Binary-outcome measurement; Quantum standard limit; Mach–Zehnder interferometer; Quantum metrology
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2022.106051

As the simplest phase estimation protocol, the inversion estimator has been widely adopted in the quantum metrology, since its performance can be simply quantified by the error-propagation formula. For a general binary-outcome measurement, we show that both the inversion estimator and the maximum likelihood estimator are the same and can asymptotically saturate the Cramér-Rao lower bound. These observations are applied to the parity detection and the zero-nonzero photon counting that have achieved super-resolved phase measurement near the shot-noise phase sensitivity in a coherent-state light Mach–Zehnder interferometer. We numerically show that the phase uncertainty almost follows the theoretical prediction of the lower bound. At the optimal working point, the best sensitivities also reach their associated analytic results for the two binary-outcome measurement schemes.
•An approximate expression of the maximum likelihood estimator (MLE) has been derived.•Both of them can saturate the CRB for any kind of the binary-outcome measurement.•This observation is applied to the phase measurement of coherent-light interferometer.