Strange Weak Values

Abstract

We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a negative weak value of a given projection operator and strange values of an observable in general. The general framework is applied to Hardy's paradox and the spin $1/2$ system to explicitly address the issues of counter-factuality and strange weak values. The counter-factual arguments which characterize the paradox specifies the pre-selected state and a complete set of the post-selected states clarifies how the strange weak values emerge.

17 pages, 1 figures, to appear in Journal of Physics A

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• Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over paths
• A weak-value model for virtual particles supplying the electric current in graphene: the minimal conductivity and the Schwinger mechanism