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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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Cite

BibTeXRIS
BibTeX
@misc{mastiukova2026reservoir,
  title = {{Reservoir Support Sets the Minimum Loss for Non-Hermitian Dynamics}},
  author = {Alena Mastiukova},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13496},
  eprint = {2609.13496},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13496},
}
RIS
TY  - UNPB
TI  - Reservoir Support Sets the Minimum Loss for Non-Hermitian Dynamics
AU  - Alena Mastiukova
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13496
UR  - https://arxiv.org/abs/2609.13496
AB  - 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.
ER  -