The Reconstruction Problem and Weak Quantum Values
  Quantum Mechanical weak values are an interference effect measured by the cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states, leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase space. We show that the knowledge of {\rho}_{{\phi},{\psi}}(z) and of one of the two functions {\phi},{\psi} unambiguously determines the other, thus generalizing a recent reconstruction result of Lundeen and his collaborators. 
Maurice de Gosson, Serge de Gosson
math-ph math.MP quant-ph