Sufficient conditions for uniqueness of the weak value

Abstract

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.

17 pages, final published response

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• Quantum instruments as a foundation for both states and observables
• Simple understanding of quantum weak values
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• Disturbance in weak measurements and the difference between quantum and classical weak values
• Weak values are quantum: you can bet on it
• Amplification of Gravitationally Induced Entanglement
• Interpreting weak value amplification with a toy realist model
• Anomalous weak values are caused by disturbance
• Counterexample to "Sufficient Conditions for uniqueness of the Weak Value" by J. Dressel and A. N. Jordan, arXiv:1106.1871v1
• Proof gap in "Sufficient conditions for uniqueness of the Weak Value" by J. Dressel and A. N. Jordan, J. Phys. A 45 (2012) 015304