  Quantum interferometry uses quantum resources to improve phase estimation
with respect to classical methods. Here we propose and theoretically
investigate a new quantum interferometric scheme based on three-dimensional
waveguide devices. These can be implemented by femtosecond laser waveguide
writing, recently adopted for quantum applications. In particular, multiarm
interferometers include "tritter" and "quarter" as basic elements,
corresponding to the generalization of a beam splitter to a 3- and 4-port
splitter, respectively. By injecting Fock states in the input ports of such
interferometers, fringe patterns characterized by nonclassical visibilities are
expected. This enables outperforming the quantum Fisher information obtained
with classical fields in phase estimation. We also discuss the possibility of
achieving the simultaneous estimation of more than one optical phase. This
approach is expected to open new perspectives to quantum enhanced sensing and
metrology performed in integrated photonic.
