Local Reservoir Constraints Add Over 1.01265 Quanta Excess Noise in Uniform Broadband Quantum Amplifier Chains

The arXiv preprint constructs adjacent-site loss channels that achieve the known single-frequency minimum only when local compatibility conditions hold. For specified uniform and dimerized chains the authors compare fixed reservoirs against matched drift, ports, high-gain band and complete gain/loss rate caps. At the representative cap R=8 they quantify how finite-band suppression forces excess noise once couplings are restricted to nearest neighbors, with boundary-response bounds showing that range-two couplings become necessary to restore performance. These calculations directly inform noise budgets for a proposed cryogenic microwave array targeting a 100 kHz design band.

The work extends prior quantum amplifier theory by replacing single-frequency optima with explicit finite-band integrals under locality. Earlier studies on directional amplifiers and reservoir engineering established the unrestricted quantum limit but left open how fixed local couplings degrade broadband performance; this paper closes that gap with explicit arithmetic averages over the band. The >1.01265 quanta penalty at N=64 is not merely numerical but indicates that nearest-neighbor designs cannot simultaneously satisfy gain flatness and noise targets without auxiliary modes or longer-range interactions.

Context from related microwave quantum-optics experiments shows that reservoir engineering in circuit QED has already demonstrated sub-quantum-limited added noise at single frequencies, yet scaling to arrays introduces precisely the locality constraints modeled here. The paper's finite-auxiliary calculations at N=64 retain a noise advantage only when total coupling budgets are matched, underscoring that hardware implementations must trade interaction range against fabrication complexity.

Next steps include mapping the derived response bounds onto concrete superconducting-circuit parameters and testing whether range-two couplers reduce the excess noise below 0.5 quanta in a 64-site prototype within the 100 kHz band.