Sufficient conditions for uniqueness of the weak value

We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average using the contextual values formalism introduced in Dressel, Agarwal and Jordan (2010 Phys. Rev. Lett. 104 240401). We also respond to criticism of our work by...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-01, Vol.45 (1), p.15304-14
Main Authors: Dressel, J, Jordan, A N
Format: Article
Language:English
Subjects:
Conditioning
contextual values
Exact sciences and technology
Formalism
Mathematical analysis
Physics
Theorems
Uniqueness
uniqueness conditions
weak values
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Summary:We review and clarify the sufficient conditions for uniquely defining the generalized weak value as the weak limit of a conditioned average using the contextual values formalism introduced in Dressel, Agarwal and Jordan (2010 Phys. Rev. Lett. 104 240401). We also respond to criticism of our work by Parrott (arXiv:1105.4188v1) concerning a proposed counter-example to the uniqueness of the definition of the generalized weak value. The counter-example does not satisfy our prescription in the case of an underspecified measurement context. We show that when the contextual values formalism is properly applied to this example, a natural interpretation of the measurement emerges and the unique definition in the weak limit holds. We also prove a theorem regarding the uniqueness of the definition under our sufficient conditions for the general case. Finally, a second proposed counter-example by Parrott (arXiv:1105.4188v6) is shown not to satisfy the sufficiency conditions for the provided theorem.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/1/015304