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PreprintarXiv licencearXiv

Time-optimal quantum dynamics under fixed-norm generators

  • Oskar A. Prośniak
  • Karol Życzkowski
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Abstract

We investigate the dynamics of quantum systems whose evolution is governed by linear generators of fixed unitarily invariant norm. For this broad class of evolutions, we derive a universal time-optimal generator of the dynamics converting one given state into another. It provides a time-optimal non-Hermitian Hamiltonian for pure state conversion. We then use this general result to derive quantum speed limits for mixed-state evolutions governed by Lindbladians and non-Hermitian Hamiltonians. Our findings follow from the geometric properties of the group GL(n,ℂ), in particular the geodesic distance. The derived bounds hold for an arbitrary system size n, depend only on the norms of the evolution generator and the initial and final states, and do not require performing any time-averaging.

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Cite

BibTeXRIS
BibTeX
@misc{prosniak2026timeoptimal,
  title = {{Time-optimal quantum dynamics under fixed-norm generators}},
  author = {Oskar A. Prośniak and Karol Życzkowski},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.42131},
  eprint = {2610.42131},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.42131},
}
RIS
TY  - UNPB
TI  - Time-optimal quantum dynamics under fixed-norm generators
AU  - Oskar A. Prośniak
AU  - Karol Życzkowski
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.42131
UR  - https://arxiv.org/abs/2610.42131
AB  - We investigate the dynamics of quantum systems whose evolution is governed by linear generators of fixed unitarily invariant norm. For this broad class of evolutions, we derive a universal time-optimal generator of the dynamics converting one given state into another. It provides a time-optimal non-Hermitian Hamiltonian for pure state conversion. We then use this general result to derive quantum speed limits for mixed-state evolutions governed by Lindbladians and non-Hermitian Hamiltonians. Our findings follow from the geometric properties of the group GL(n,ℂ), in particular the geodesic distance. The derived bounds hold for an arbitrary system size n, depend only on the norms of the evolution generator and the initial and final states, and do not require performing any time-averaging.
ER  -