Counterexample to "Sufficient Conditions for uniqueness of the Weak Value" by J. Dressel and A. N. Jordan, arXiv:1106.1871v1

Stephen Parrott

Published 2011-05-20, updated 2012-10-15Version 7

The abstract of "Contextual Values of Observables in Quantum Measurements" by J. Dressel, S. Agarwal, and A. N. Jordan [Phys. Rev. Lett. 104 240401 (2010)] (called DAJ below), states: "We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general conditioned average that converges uniquely to the quantum weak value in the minimal disturbance limit." A counterexample to the claim of the last sentence was presented in Version 1. Subsequently Dressel and Jordan placed in the arXiv the paper of the title (called DJ below) which attempts to prove the claim of DAJ quoted above under stronger hypotheses than given in DAJ, hypotheses which the counterexample does not satisfy. The present work (Version 6) presents a new counterexample to this revised claim of DJ. A brief introduction to "contextual values" is included. Also included is a critical analysis of DJ.