Overcoming Fabrication Llimits in Integrated PNRDs with a Mixed-Efficiency Linear Multiplexing Scheme

We present a photon-number resolving detector that merges variable- and fixed-efficiency single-photon detectors in one linear array. After a first, optimized section for high absorption, extra detectors with the minimum efficiency allowed by fabrication are added. Analytical and numerical tools show how the fidelity of variable-, uniform- and hybrid-efficiency arrays changes, while keeping the design manufacturable on lithium-niobate photonic circuits equipped with niobium-nitride nanowires. This scheme offers a realistic route to scalable, chip-level photon counting for quantum communication, computing and sensing.