Symmetries and entanglement features of inner-mode resolved correlations of interfering nonidentical photons

Multiphoton quantum interference underpins fundamental tests of quantum mechanics and quantum technologies. Consequently, the detrimental effect of photon distinguishability in multiphoton interference experiments can be catastrophic. Here we employ correlation measurements in the photonic inner modes, time or frequency, to restore quantum interference between photons differing in their colors or injection times in arbitrary linear optical networks, without the need for additional filtering or postselection. Interestingly, we demonstrate how harnessing the multiphoton inner-mode quantum information enables us to infer information about symmetries of multiphoton networks and states and to observe arbitrary degrees of W-state entanglement between a small number of photons with a fixed interferometer. These results are therefore of profound interest for future applications of universal inner-mode-resolved linear optics across fundamental science and quantum technologies with photons with experimentally different spectral properties.