Ergodic Theorems for Quantum Trajectories under Disordered Generalized Measurements
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912210493636608 |
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| author | Ekblad, Owen Moreno-Nadales, Eloy Pathirana, Lubashan |
| author_facet | Ekblad, Owen Moreno-Nadales, Eloy Pathirana, Lubashan |
| contents | We consider quantum trajectories arising from disordered, repeated generalized measurements, which have the structure of Markov chains in random environments (MCRE) with dynamically-defined transition probabilities; we call these disordered quantum trajectories. Under the assumption that the underlying disordered open quantum dynamical system approaches a unique equilibrium in time averages, we establish a strong law of large numbers for measurement outcomes arising from disordered quantum trajectories, which follows after we establish general annealed ergodic theorems for the corresponding MCRE. The type of disorder our model allows includes the random settings where the disorder is i.i.d. or Markovian, the periodic (resp. quasiperiodic) settings where the disorder has periodic (resp. quasiperiodic) structure, and the nonrandom setting where the disorder is constant through time. In particular, our work extends the earlier noise-free results of Kümmerer and Maassen to the present disordered framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodic Theorems for Quantum Trajectories under Disordered Generalized Measurements Ekblad, Owen Moreno-Nadales, Eloy Pathirana, Lubashan Mathematical Physics Quantum Physics We consider quantum trajectories arising from disordered, repeated generalized measurements, which have the structure of Markov chains in random environments (MCRE) with dynamically-defined transition probabilities; we call these disordered quantum trajectories. Under the assumption that the underlying disordered open quantum dynamical system approaches a unique equilibrium in time averages, we establish a strong law of large numbers for measurement outcomes arising from disordered quantum trajectories, which follows after we establish general annealed ergodic theorems for the corresponding MCRE. The type of disorder our model allows includes the random settings where the disorder is i.i.d. or Markovian, the periodic (resp. quasiperiodic) settings where the disorder has periodic (resp. quasiperiodic) structure, and the nonrandom setting where the disorder is constant through time. In particular, our work extends the earlier noise-free results of Kümmerer and Maassen to the present disordered framework. |
| title | Ergodic Theorems for Quantum Trajectories under Disordered Generalized Measurements |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2501.18014 |