Overcomplete quantum tomography of a path-entangled two-photon state

Path-entangled N-photon states are key resources for quantum enhanced metrology and quantum imaging, as well as quantum computation. However, the quantum tomography of path-entangled indistinguishable photons is still in its infancy. We propose and implement a quantum tomographical method to characterize path-entangled two-photon NOON states, which can be extended to arbitrary N. To access both the populations and the coherences of the path-encoded density matrix, a single ancilla spatial mode is introduced, and photon correlations are performed as a function of a single phase within an interferometer. We characterize a two-photon state generated through the Hong-Ou-Mandel interference of indistinguishable single photons emitted by a semiconductor quantum dot and show that an overcomplete data set reveals spatial coherences that could be otherwise hidden due to limited statistics. We finally extract the truly indistinguishable part of the density matrix and identify the main origin for the reduced degree of entanglement.