Abstract
A weak value is an effective description of the influence of a pre and post-selected ‘principal’ system on another ‘meter’ system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and deflections in otherwise unperturbed variables: this motivates investigation of the potential benefits of the protocol in precision metrology. We present a visual interpretation of weak value experiments in phase space, enabling an evaluation of the effects of three types of detector noise as ‘Fisher information efficiency’ functions. These functions depend on the marginal distribution of the Wigner function of the ‘meter’, and give a unified view of the weak value protocol as a way of protecting Fisher information from detector imperfections. This approach explains why weak value techniques are more effective for avoiding detector saturation than for mitigating detector jitter or pixelation.
Highlights
Professor Izumi Tsutsui has identified three categories of research into weak values [1]
Using the Wigner representation of the meter to describe weak value experiments, we have provided a simple picture of the flexibility of the method and how it compares to standard measurements
Working with real Gaussian meter states and in the linear regime considered by Albert and Vaidman (AAV), we have extended previous arguments [19] concerning the Fisher information about the coupling parameter between system and meter: allowing for arbitrary complex weak values and measurements at oblique angles in phase space
Summary
Professor Izumi Tsutsui has identified three categories of research into weak values [1]. There is the issue of technical noise: as long as post-selection is performed in the experiment before any ultimate detection (say with a polariser), rather than merely implemented as voluntary data loss, the weak value technique has characteristics that physically distinguish it from regular approaches. This means that certain types of detector noise may favour one approach over the other, potentially reversing the conclusions reached for ideal detection: it is difficult to say in full generality when advantages may be had, and the situation must be judged mostly on a caseby-case basis. In our treatment of three types of technical noise—namely transverse jitter, pixelation and saturation—we rely heavily on theoretical results that have been previously reported [6,19,25] but require some re-application in our new setting
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