Robustness of homodyne tomography to phase-insensitive noise

Imprinting Complete Information about a Quantum Channel on its Output State

“…Notice that unboundedness of the map inversion can even wash out completely the information on the channel in some particular chosen representation B fB j g, e.g., when all operators B j are out of the boundedness domain of R ÿ1 . This is the case, for example, of the (overcomplete) representation B fjihjg, with ji and ji coherent states, since from the identity which has convergence radius 1 2 , which is the wellknown bound for Gaussian noise for the quantum tomographic reconstruction for coherent-state and Fock representations [13]. Therefore, we say that the state is formally faithful, however, we are constrained to representations which are analytical for the inverse map R ÿ1 .…”