Systems that saturate the Margolus-Levitin quantum speed limit
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908832922337280 |
|---|---|
| author | Sönnerborn, Ole |
| author_facet | Sönnerborn, Ole |
| contents | We provide a complete characterization of all finite-dimensional quantum systems that saturate the Margolus-Levitin quantum speed limit at arbitrary Uhlmann-Jozsa fidelity. Employing a purification-based approach, we prove that mixed-state saturation occurs precisely when three structural criteria are fulfilled: the state's support is confined to the sum of two energy eigenspaces (the ground level and a single excited level); each eigenvector of the state with nonzero weight is a fixed superposition of one ground- and one excited-state energy eigenvector (determined by the minimizer of the objective function identified by Giovannetti et al.) and all such eigenvectors evolve in mutually orthogonal subspaces. These requirements impose a strict rank bound, ruling out saturation by any faithful state. For quantum bits, we derive a purity-resolved and tight Margolus-Levitin bound that reduces to the pure-state result in the limit of unit purity. Through a time-reversal argument, we further extend the dual Margolus-Levitin quantum speed limit to mixed states and establish the corresponding saturation conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Systems that saturate the Margolus-Levitin quantum speed limit Sönnerborn, Ole Quantum Physics We provide a complete characterization of all finite-dimensional quantum systems that saturate the Margolus-Levitin quantum speed limit at arbitrary Uhlmann-Jozsa fidelity. Employing a purification-based approach, we prove that mixed-state saturation occurs precisely when three structural criteria are fulfilled: the state's support is confined to the sum of two energy eigenspaces (the ground level and a single excited level); each eigenvector of the state with nonzero weight is a fixed superposition of one ground- and one excited-state energy eigenvector (determined by the minimizer of the objective function identified by Giovannetti et al.) and all such eigenvectors evolve in mutually orthogonal subspaces. These requirements impose a strict rank bound, ruling out saturation by any faithful state. For quantum bits, we derive a purity-resolved and tight Margolus-Levitin bound that reduces to the pure-state result in the limit of unit purity. Through a time-reversal argument, we further extend the dual Margolus-Levitin quantum speed limit to mixed states and establish the corresponding saturation conditions. |
| title | Systems that saturate the Margolus-Levitin quantum speed limit |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.23237 |