Remote state preparation and teleportation in phase space

Continuous variable remote state preparation and teleportation are analysed using Wigner functions in phase space. We suggest a remote squeezed state preparation scheme between two parties sharing an entangled twin beam, where homodyne detection on one beam is used as a conditional source of squeezing for the other beam. The scheme also works with noisy measurements, and provides squeezing if the homodyne quantum efficiency is larger than 50%. The phase space approach is shown to provide a convenient framework to describe teleportation as a generalized conditional measurement, and to evaluate relevant degrading effects, such the finite amount of entanglement, the losses along the line and the nonunit quantum efficiency at the sender location.