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

[en] 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.

Disciplines :

Physics

Author, co-author :

HÖRNEDAL, Niklas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

PROSNIAK, Oskar ; University of Luxembourg

DEL CAMPO ECHEVARRIA, Adolfo ; University of Luxembourg ; Donostia International Physics Center, E-20018 San Sebastián, Spain

CHENU, Aurélia ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

External co-authors :

yes

Language :

English

Title :

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

Publication date :

05 May 2025

Journal title :

Quantum

eISSN :

2521-327X

Publisher :

Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften

Volume :

Pages :

1729

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://quantum-journal.org/papers/q-2025-05-05-1729/pdf/

Funders :

Luxembourg National Research Fund

Available on ORBilu :

since 20 June 2025

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