"Contextual weak values" of quantum measurements with positive measurement operators are not limited to the traditional weak value
arXiv:1102.4407
Abstract
A recent Letter in Physical Review Letters, "Contextual Values of Observables in Quantum Measurements", by J. Dressel, S. Agarwal, and A. N. Jordan (abbreviated DAJ below), introduces the concept of "contextual values" and claims that they lead to "a natural definition of a general conditioned average that converges uniquely to the quantum weak value in the minimal disturbance limit". However, they do not define "minimal disturbance limit". The present paper is in part the saga of my search for a definition of "minimal disturbance limit" under which this claim could be proved. The search finally ended in what is probably a definitive counterexample to the claim.
32 pages, LaTeX. Version 4 has a new title and abstract. It consist of an essentially unaltered Version 3 with the addition of a counterexample to one of the main results of [J. Dressel, S. Agarwal, and A. N. Jordan, Phys. Rev. Lett. 104, 240401 (2010)]. Version 5 is mathematically identical except that a major typo in equation (133) has been corrected. Version 6 corrects minor typos