Configurable and scalable continuous variable (CV) quantum networks for measurement-based quantum information protocols or multipartite quantum communication schemes can be obtained via parametric down conversion (PDC) in non-linear waveguides. In this work, we exploit symmetric group velocity matching (SGVM) to engineer the properties of the squeezed modes of the PDC. We identify type II PDC in a single waveguide as the best suited process, since multiple modes with non-negligible amount of squeezing can be obtained. We explore, for the first time, the waveguide dimensions, usually only set to ensure single-mode guiding, as an additional design parameter ensuring indistinguishability of the signal and idler fields. We investigate here potassium titanyl phosphate (KTP), which offers SGVM at telecommunications wavelengths, but our approach can be applied to any non-linear material and pump wavelength. This work paves the way toward the engineering of future large-scale quantum networks in the CV regime.

Spectro-temporal modes of light can be exploited for the generation of high-dimensional Gaussian quantum states. Such states are at the basis of continuous variable quantum information protocols where they have to support mode-selective non-Gaussian operations. We develop a general framework for single-photon addition on multimode states of light via parametric down conversion (PDC) processes. We identify the analytical conditions for single-mode and mode-selective photon addition. We show that spectral mode selectivity can be achieved in the type-II collinear down conversion, while single-mode condition are retrieved for noncollinear type-I and type-II processes. Numerical results are shown for photon addition in PDC process at near-infrared and telecommunications wavelengths.