Toolbox for continuous-variable entanglement production and measurement using spontaneous parametric down-conversion

We provide a toolbox for continuous-variable quantum-state engineering and characterization of biphoton states produced by spontaneous parametric down-conversion in a transverse pump configuration. We show that the control of the pump beam's incidence spot and angle corresponds to phase-space displacements of conjugate collective continuous variables of the biphoton. In particular, we illustrate with numerical simulations on a semiconductor device how this technique can be used to engineer and characterize arbitrary states of the frequency and time degrees of freedom.