The reconstruction problem and weak quantum values

Quantum mechanical weak values are an interference effect measured by the cross-Wigner transform W(φ,ψ) of the post- and pre-selected states, leading to a complex quasi-distribution ρφ,ψ(x, p) on phase space. We show that the knowledge of ρφ,ψ(z) and of one of the two functions φ, ψ unambiguously determines the other, thus generalizing a recent reconstruction result of Lundeen and his collaborators. (paper)