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arXiv · 2609.13496

Reservoir Support Sets the Minimum Loss for Non-Hermitian Dynamics

Alena Mastiukova
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Abstract

The minimum loss required to reproduce non-Hermitian dynamics depends on how many physical modes each reservoir can address coherently. Established positive-matrix criteria bound this cost. We construct a phase-controlled cubic-root Su-Schrieffer-Heeger chain in which three-mode reservoirs attain the unrestricted passivity threshold throughout its phase diagram and halve the minimum pair-supported loss at a tuned point. The bound constrains exact conditional trajectories, including time-dependent Markov controls, rather than preparation of one final state. A connected-chain protocol tests effective reservoir support through calibrated finite-time emission. Full system-auxiliary propagation then bounds conditional fidelity and target yield for every one-particle input. A coherent controller that accurately prepares the selected endpoint fails this propagator test. A singular-value bound excludes every unitary realization of the same conditional map. These results connect local reservoir access to a measurable loss cost for prescribed dynamics.

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Alena Mastiukova. 2026-09-11. Reservoir Support Sets the Minimum Loss for Non-Hermitian Dynamics. https://arxiv.org/abs/2609.13496

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