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Heralded processes on continuous-variable spaces as quantum maps

Heralding processes, which only work when a measurement on a part of the system give the good result, are particularly interesting for continuous-variables. They permit non-Gaussian transformations that are necessary for several continuous-variable quantum information tasks. However if maps and quantum process tomography are commonly used to describe quantum transformations in discrete-variable space, they are much rarer in the continuous-variable domain. Also, no convenient tool for representing maps in a way more adapted to the particularities of continuous variables have yet been explored. In this paper we try to fill this gap by presenting such a tool.