Distinct Feedback-Strength Requirements for Quantum-State Ensemble Preparation under Channel-Equivalent Monitoring

Abstract:Different measurements of the same environment can preserve the average quantum channel yet change the feedback strength needed to prepare a state ensemble. We establish this distinction for a multiqubit register under complete Pauli monitoring, targeting the uniform ensemble of real-amplitude pure states. With unit detection efficiency, public records, and bounded Hamiltonian feedback, fixed transverse noise requires a minimum peak strength proportional to $\epsilon^{-1}$ at distributional error $\epsilon$. Tangent noise instead admits a construction requiring only $O[\sqrt{\log(1/\epsilon)}]$. At fixed preparation time, we determine the optimum over all allowed feedback policies and derive a geometric lower bound beyond radial symmetry. The separation identifies the measurement realization as part of the control-resource specification for monitored ensemble preparation.

arXiv:2609.31221 [quant-ph]

(or arXiv:2609.31221v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.31221 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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