Quantum Reciprocity: A Structured-Bath Hamiltonian for Coherent Amplification
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Abstract
Macroscopic quantum amplifiers maintain coherence even while strongly coupled to their surroundings, demonstrating that coherence can be preserved through architecture rather than isolation. Here we derive a finite structured-bath Hamiltonian in which dissipation and feedback originate from the same microscopic couplings. The resulting self-energy Σ(ω) exhibits coupled real and imaginary parts whose evolution reproduces the breathing dynamics observed in Josephson quantum amplifiers. This establishes quantum reciprocity: macroscopic coherence lives not in isolation, but in structured connection. We numerically validate this principle by engineering a six-qubit structured bath to demonstrate controllable transitions from dissipation to amplification. This architectural core serves as the foundation for a proposed multi-scale workflow to transform quantum noise into a design resource, preserving coherence not through isolation but through architectural reciprocity.