Fisher information vs. signal-to-noise ratio for a split detector

Abstract

We study the problem of estimating the magnitude of a Gaussian beam displacement using a two pixel or 'split' detector. We calculate the maximum likelihood estimator, and compute its asymptotic mean-squared-error via the Fisher information. Although the signal-to-noise ratio is known to be simply related to the Fisher information under idealised detection, we find the two measures of precision differ markedly for a split detector. We show that a greater signal-to-noise ratio 'before' the detector leads to a greater information penalty, unless adaptive realignment is used. We find that with an initially balanced split detector, tuning the normalised difference in counts to 0.884753... gives the highest posterior Fisher information, and that this provides an improvement by at least a factor of about 2.5 over operating in the usual linear regime. We discuss the implications for weak-value amplification, a popular probabilistic signal amplification technique.

9 pages, 2 figures

References in corpus (7)

• Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts
• Technical advantages for weak value amplification: When less is more
• Measuring ultrasmall time delays of light by joint weak measurements
• When amplification with weak values fails to suppress technical noise
• Quantum limits in the measurement of very small displacements in optical images

Cited by in corpus (4)

• Precision optical displacement measurements using biphotons
• A Fundamental Upper Bound for Signal to Noise Ratio of Quantum Detectors
• Weak-measurement-based pseudospin pointer: A cost-effective scheme for precision measurement
• Seeing opportunity in every difficulty: protecting information with weak value techniques