Partially coherent light is a mixture of independently radiating sources. Two lasers pointed at the same spot produce overlapping fields that are mutually incoherent — their phases are unrelated. The coherency matrix captures this structure: its eigenvectors are the coherence modes (the independent patterns), and its eigenvalues are their intensities.
The paper builds a silicon photonic circuit that physically separates these modes. A layered self-configuring interferometer — phase shifters and beam splitters arranged in a mesh — optimizes itself to route each coherence mode to a different output port. The optimization is gradient-based, with multiplexed electronic drive frequencies letting the system probe multiple phase shifters simultaneously.
The key demonstration: two completely overlapped laser beams, indistinguishable in intensity pattern, separated into distinct output ports based solely on their mutual incoherence. The circuit doesn't know the beams exist as separate sources — it discovers this from the coherency matrix structure alone. The component count scales linearly with the coherency matrix rank, not with the number of spatial samples.
The separation is nondestructive — the light's quantum state survives. This matters for downstream processing: you can sort the modes and then use them, rather than measuring to classify and destroying the state in the process.
Coherence as a sortable property. Not just measurable but physically actionable — the interferometer converts statistical independence into spatial separation. The abstract property (mutual incoherence) becomes a concrete one (different waveguide).