Three Results on Weak Measurements

Abstract

Three recent results on weak measurements are presented. They are: (i) repeated measurements on a single copy cannot provide any information on it and further, that in the limit of very large such measurements, weak measurements have exactly the same characteristics as strong measurements; (ii) the apparent non-invasiveness of weak measurements is illusory and they are no more advantageous than strong measurements even in the specific context of establishing Leggett-Garg inequalities, when errors are properly taken into account, and, finally, (iii) weak value measurements are optimal, in the precise sense of Wootters and Fields, when the post-selected states are mutually unbiased with respect to the eigenstates of the observable whose weak values are being measured. Notion of weak value coordinates for state spaces are introduced and elaborated.