The rate of purification of quantum trajectories
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911387226210304 |
|---|---|
| author | Bompais, Maël Amini, Nina H. Garrahan, Juan P. Guţă, Mădălin |
| author_facet | Bompais, Maël Amini, Nina H. Garrahan, Juan P. Guţă, Mădălin |
| contents | We investigate the behavior of quantum trajectories conditioned on measurement outcomes. Under a condition related to the absence of so-called dark subspaces, Kümmerer and Maassen had shown that such trajectories almost surely purify in the long run. In this article, we first present a simple alternative proof of this result using Lyapunov methods. We then strengthen the conclusion by proving that purification actually occurs at an exponential rate in expectation, again using a Lyapunov approach. Furthermore, we address the quantum state estimation problem by propagating two trajectories under the same measurement record--one from the true initial state and the other from an arbitrary initial guess--and show that the estimated trajectory converges exponentially fast to the true one, thus quantifying the rate at which information is progressively revealed through the measurement process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14023 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The rate of purification of quantum trajectories Bompais, Maël Amini, Nina H. Garrahan, Juan P. Guţă, Mădălin Quantum Physics Mathematical Physics We investigate the behavior of quantum trajectories conditioned on measurement outcomes. Under a condition related to the absence of so-called dark subspaces, Kümmerer and Maassen had shown that such trajectories almost surely purify in the long run. In this article, we first present a simple alternative proof of this result using Lyapunov methods. We then strengthen the conclusion by proving that purification actually occurs at an exponential rate in expectation, again using a Lyapunov approach. Furthermore, we address the quantum state estimation problem by propagating two trajectories under the same measurement record--one from the true initial state and the other from an arbitrary initial guess--and show that the estimated trajectory converges exponentially fast to the true one, thus quantifying the rate at which information is progressively revealed through the measurement process. |
| title | The rate of purification of quantum trajectories |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2601.14023 |