Christopher Ferrie, Joshua Combes
For the task of parameter estimation, we show using statistically rigorous arguments that the process of postselection (a pre-requisite for so-called weak value amplification) can be no better on average than performing inference using all data. Moreover, we show that the probability of obtaining better estimates using postselection decreases exponentially with the number of measurements. Finally, we argue that, even in the regime where weak values are traditionally relevant, estimation using the maximum likelihood technique with weak values as small as possible produces better performance for quantum metrology. We also show these conclusions do not change in the presence of technical noise.
View original:
http://arxiv.org/abs/1307.4016
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