Spatiotemporal effects in heralded state preparation

Heralding, which is often used for preparing quantum optical states, is studied to determine the effects of the spatiotemporal properties of the process. Incorporating all the spatiotemporal degrees of freedom, we follow a Wigner functional approach to consider cases where these states are prepared to have Wigner functionals with negative regions, being suitable resources for quantum information technologies. General expressions are derived for single-photon-subtracted and single-photon-added states. As examples, we consider the photon-subtracted squeezed vacuum state, the photon-added coherent state, the photon-added thermal state, and the photon-added squeezed vacuum state. The Wigner functional approach reveals the importance of the spatiotemporal transformations imposed by the experimental conditions.