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A photonic circuit is generally described as a structure in which light propagates by unitary exchange and transfers reversibly between channels. In contrast, the term 'diffusive' is more akin to a chaotic propagation in scattering media, where light is driven out of coherence towards a thermal mixture. Based on the dynamics of open quantum systems, the combination of these two opposites can result in novel techniques for coherent light control. The crucial feature of these photonic structures is dissipative coupling between modes, via an interaction with a common reservoir. Here, we demonstrate experimentally that such systems can perform optical equalisation to smooth multimode light, or act as a distributor, guiding it into selected channels. Quantum thermodynamically, these systems can act as catalytic coherent reservoirs by performing perfect non-Landauer erasure. For lattice structures, localised stationary states can be supported in the continuum, similar to compacton-like states in conventional flat-band lattices.

We predict a linear nonreciprocal effect that is based on the timed Dicke states in an ensemble of dipole-dipole coupled oscillators. This effect is examined on a nanoscale antenna array comprising two-level identical emitters. The studied nonreciprocity, which has no analogs in classical antennas, manifests itself in strong characteristic asymmetry of the radiation pattern, even for a single-photon laser pumping. Promising applications of our results for remotely tunable nanoantennas and nanocircuit elements are discussed.