Three results on weak measurements

TL;DR

This paper discusses three key results on weak measurements, showing their limitations, non-invasiveness is illusory, and their optimality under specific conditions, with implications for quantum measurement theory.

Contribution

It presents three new findings on weak measurements, clarifying their limitations, non-invasiveness, and optimality conditions, advancing understanding in quantum measurement theory.

Findings

Repeated measurements on a single copy provide no information.

Weak measurements are not more advantageous than strong ones when errors are considered.

Weak value measurements are optimal for mutually unbiased post-selected states.

Abstract

Three recent results on weak measurements are presented. They are: i) repeated measurements on a single copy can not provide any information on it and further, that in the limit of very large such measurements, weak measurements have exactly the same characterstics as strong measurements, ii) the apparent non-invasiveness of weak measurements is \emph{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.