Quantum multiphoton interference in position and in linear momentum spaces

Since its first observation, multiphoton interference has been largely implemented in different quantum fields, such as quantum computing and quantum communication. This phenomenon is connected to the bosonic nature of photons and it is the core of quantum advantage in several applications. This PhD thesis investigates multiphoton interference using three different photonic platforms: bulk, i.e. the photons travel in free air or in silicon fiber; photonic integrated circuits, i.e. optical waveguides written in glass that make possible to implement tunable beamsplitters and phase shifters; and g-plates, which are novel liquid-crystal devices, that acts on the linear momentum space of photons, according to their polarization states. These reconfigurable platforms are exploited to perform indistinguishability tests on output states, three- and four-photon Boson Sampling experiments and three-step two-dimensional quantum walk evolutions, respectively. Finally, the versatility of the g-plate platform is exploited to engineer single-photon states in linear momentum of the light. We provide a set of reconfigurable platforms that pave the way for future and more complex experiments where an increasing number of inputs, evolution modes as well as outputs can be enlarged. In particular, we benchmark a reconfigurable photonic chip for future realizations of Boson Sampling variant as Gaussian Boson Sampling. The g-plate platform in linear momentum of the light can also realize qudit states for quantum cryptography application as the engineering of a set of mutually unbiased bases in high dimensional Hilbert space to increase the security of the protocol.