The Hong-Ou-Mandel interferometer is a foundational tool in quantum optics with both fundamental and practical significance. Earlier works identified that input-state symmetry under exchange of the two spatial modes is fundamental in the understanding of the Hong-Ou-Mandel effect. We now show that this notion of symmetry is central to generalizing this effect. In particular, this point of view enables the construction of extensions beyond the standard two single-photon case to arbitrary input states, as well as to configurations with more than two spatial modes via a natural generalization of the beam splitter to a discrete Fourier transform interferometer. Beyond its conceptual significance, this framework offers direct insights into quantum metrology, showing how symmetry properties of input states allow for the computation of explicit precision bounds. By focusing on symmetry, we provide a perspective that simplifies and unifies a range of known results while paving the way for new developments in quantum interference and sensing.

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• Optical interferometry
• Quantum metrology
• Quantum optics