Characterization of tomographically faithful states in terms of their Wigner function

A bipartite quantum state is tomographically faithful when it can be used as an input of a quantum operation acting on one of the two quantum systems, such that the joint output state carries a complete information about the operation itself. Tomographically faithful states are a necessary ingredient for tomography of quantum operations and for complete quantum calibration of measuring apparatuses. In this paper we provide a complete classification of such states for continuous variables in terms of the Wigner function of the state. For two-mode Gaussian states faithfulness simply resorts to correlation between the modes.