The Role of Symmetry in Generalized Hong-Ou-Mandel Interference and Quantum Metrology

TL;DR

This paper explores how symmetry underpins the generalization of Hong-Ou-Mandel interference to complex multi-mode quantum states and links these symmetries to enhanced quantum metrology precision bounds.

Contribution

It introduces a symmetry-based framework for extending Hong-Ou-Mandel interference to multiple modes and input states, unifying existing results and enabling new quantum sensing strategies.

Findings

Symmetry properties determine interference effects.

Explicit quantum precision bounds are derived from symmetry.

Framework generalizes to multi-mode and multi-photon states.

Abstract

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 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.