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Weak-Value Amplification And Optimal Parameter Estimation In The Presence Of Correlated Noise, Josiah Sinclair, Matin Hallaji, Aephraim M. Steinberg, Jeff Tollaksen, Andrew N. Jordan

Mathematics, Physics, and Computer Science Faculty Articles and Research

We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement strategy that involves sorting data into separate subsets based on the outcome of a second “partitioning” measurement. Using a simplified correlated noise model that can be analyzed exactly together with optimal statistical estimators, we compare WVA to a conventional measurement method. We find that WVA indeed yields a much lower variance of the parameter of interest than the conventional technique does, optimized in the absence of any partitioning …