A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators

Niklas Hörnedal; Oskar A. Prośniak; Adolfo del Campo; Aurélia Chenu

doi:10.22331/q-2025-05-05-1729

A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators

Niklas Hörnedal¹, Oskar A. Prośniak¹, Adolfo del Campo^1,2, and Aurélia Chenu¹

¹Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, G. D. Luxembourg
²Donostia International Physics Center, E-20018 San Sebastián, Spain

Published:	2025-05-05, volume 9, page 1729
Editor:	Ivan Contreras
Eprint:	arXiv:2405.13913v2
Doi:	https://doi.org/10.22331/q-2025-05-05-1729
Citation:	Quantum 9, 1729 (2025).

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Abstract

Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and incoherent directions and provide their physical interpretation. This understanding enables us to optimize the success rate of non-Hermitian driving along prescribed trajectories, with direct relevance to shortcuts to adiabaticity. Next, we explore the geometric interpretation of a speed limit for non-Hermitian Hamiltonians and analyze its tightness. We derive the explicit expression that saturates this bound and illustrate our results with a minimal example of a dissipative qubit.

Featured image: The image depicts the shortest Bures geodesic between two mixed states $\rho_1$ and $\rho_2$, which can be traversed via non-Hermitian dynamics. This evolution saturates a quantum speed limit, establishing a lower bound on the evolution time.

► BibTeX data

@article{Hornedal2025geometrical,
  doi = {10.22331/q-2025-05-05-1729},
  url = {https://doi.org/10.22331/q-2025-05-05-1729},
  title = {A geometrical description of non-{H}ermitian dynamics: speed limits in finite rank density operators},
  author = {H{\"{o}}rnedal, Niklas and Pro{\'{s}}niak, Oskar A. and del Campo, Adolfo and Chenu, Aur{\'{e}}lia},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1729},
  month = may,
  year = {2025}
}

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