When less is more in parameter estimation
Post date: Sep 20, 2013 7:03:14 PM
A central problem in the theory of precision measurement is how to extract the value of an unknown parameter from a collection of data that depends both on the parameter and a random variable.
It is intuitively obvious that if you choose to ignore some of that data, the statistical uncertainty of your estimate will increase, or at best remain the same. This intuition is quantified with the concept of Fisher information, which sets the minimal possible statistical uncertainty about the parameter of interest.
Recent experiments have successfully used "weak value amplification" as a metrological technique to detect a parameter more accurately. Surprisingly, this technique uses only a small fraction of the available events to make this precise measurement. How can this be? We show how this technique funnels all the information into a small fraction of the events, so all the information about the parameter can be extracted from them.
We further show there are cases where the presence of technical noise can be suppressed by the experimental set-up implementing the weak value technique. Therefore, even using the optimal statistical estimators, the weak value amplification technique can give a fundamental advantage over standard measurements for the purposes of precision measurement in the presence of technical noise sources.
Read more about it:
Technical advantages for weak value amplification: When less is more
Andrew N. Jordan, Julián Martínez-Rincón, John C. Howell
Update: This paper is now published here: