entanglement [@Politi2008; @Martin2012a; @Jin2014], quantum interference [@Silverstone2014] and boson sampling [@Crespi2013; @Spagnolo2014]. The technological challenge to combine multiple functionalities in a mutually compatible manner remains.

To date, photonic tripartite states have been generated successfully via simultaneous [@Keller1998; @Barz2010; @Guerreiro2014] and cascaded parametric down-conversion (PDC) [@Huebel2010; @Shalm2013; @Hamel2014], by cascading three- and/or four-wave mixing processes [@Jia2012; @Qin2014; @Jing2014; @Ding2015] or by using tri-exciton decays in coupled solid-state quantum dot sources [@Khoshnegar2015]. Also, the generation of photon triplets using cascaded superlattices in nonlinear crystals has been studied in detail in [@Antonosyan2011]. Due to the chosen architectures, most of the experimental approaches inherently suffer from loss at the interfaces of the involved elements, they are space-consuming and can be susceptible to long-term stability issues. Additionally, the required pump powers for photon-triplet generation are typically of the order of several milliwatts, whereas more energy-efficient systems are favorable for real-world applications.

Based on the idea of cascaded PDC [@Huebel2010], we pursue a fully monolithic approach to generate photon-triplet states on a second-order nonlinear waveguide chip. We use lithium niobate with diffused waveguide structures [@Schmidt1974; @Parameswaran2002], since they offer low loss [@Regener1985], high source brightness [@Tanzilli2001; @Krapick2013; @Krapick2014] and fast electro-optical switching capabilities [@Jin2014] for reconfigurable 