Welcome to the second day of the Paraty 2013 Workshop!
This morning, George Knee (Oxford) gave us a very entertaining and clear talk about the general approach to metrology using weak values. The main take home message was that weak values, in the presence of noise, do no better than the standard measurement method, at least if all you’re concerned about is the Fisher information, renormalized by the actual number of observed events.
This (lack of) advantage of the weak measurements seems to follow from the quantum Cramer-Rao bounds, if you consider weak measurements as a special case of POVM. This, however, is true for the case of pure states, i.e. no noise. George’s results apparently establish that the situation doesn’t change if noise is considered.
George’s criticism of many papers that use (or perhaps, hype) weak measurements is perhaps controversial. In all fairness, George was careful in pointing out that there may be other reasons why weak values could be helpful: the experimental setup may be simpler, they may help avoid detector saturation, they may be helpful in slightly different problems (such as doing full tomography with a single setup), etc. In question time, Bruno Escher (UFRJ) pointed out that at least some of the papers George referred to could only succeed by doing weak measurements, as the standard approach wouldn’t be feasible using current technology.