Quantum Reciprocity: A Structured-Bath Hamiltonian for Coherent Amplification

TL;DR

This paper introduces a structured-bath Hamiltonian that enables macroscopic quantum coherence through architectural design, demonstrating controllable dissipation and amplification in quantum systems.

Contribution

It derives a finite structured-bath Hamiltonian showing how coherence can be maintained via architecture, not isolation, and validates this with a six-qubit engineered bath.

Findings

Demonstrates controllable transition from dissipation to amplification.

Establishes quantum reciprocity principle in structured environments.

Provides a foundation for transforming quantum noise into a design resource.

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 {\Sigma}({\omega}) 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.