  Multiparameter estimation is a general problem that aims at measuring unknown
physical quantities, obtaining high precision in the process. In this context,
the adoption of quantum resources promises a substantial boost in the
achievable performances with respect to the classical case. However, several
open problems remain to be addressed in the multiparameter scenario. A crucial
requirement is the identification of suitable platforms to develop and
experimentally test novel efficient methodologies that can be employed in this
general framework. We report the experimental implementation of a
reconfigurable integrated multimode interferometer designed for the
simultaneous estimation of two optical phases. We verify the high-fidelity
operation of the implemented device, and demonstrate quantum-enhanced
performances in two-phase estimation with respect to the best classical case,
post-selected to the number of detected coincidences. This device can be
employed to test general adaptive multiphase protocols due to its high
reconfigurability level, and represents a powerful platform to investigate the
multiparameter estimation scenario.
