Sufficient conditions for uniqueness of the weak value

Details Sufficient conditions for uniqueness of the weak value Sufficient conditions for uniqueness of the weak value

2011-06-09

arxiv.org/abs/1106.1871v2

J. Phys. A: Math. Theor. 45 015304 (2012)

Physics

Quantum Physics

17 pages, final published response

Scientific paper

10.1088/1751-8113/45/1/015304

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 J, Agarwal S and Jordan A N 2010 Phys. Rev. Lett. 104, 240401. We also respond to criticism of our work in [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 in [arXiv:1105.4188v6] is shown not to satisfy the sufficiency conditions for the provided theorem.

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