Reducibility Theory and Ergodic Theorems for Ergodic Quantum Processes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918438599917568 |
|---|---|
| author | Ekblad, Owen Schenker, Jeffrey |
| author_facet | Ekblad, Owen Schenker, Jeffrey |
| contents | We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic quantum processes. This serves as a unifying framework for many models, including i.i.d., Markovian, periodic, and quasiperiodic models. We establish various characterizations of irreducibility, from which we recover a number of general ergodic theorems. We then analyze some specific examples, and, in particular, give a refinement of our theory in the i.i.d. case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reducibility Theory and Ergodic Theorems for Ergodic Quantum Processes Ekblad, Owen Schenker, Jeffrey Quantum Physics Mathematical Physics We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic quantum processes. This serves as a unifying framework for many models, including i.i.d., Markovian, periodic, and quasiperiodic models. We establish various characterizations of irreducibility, from which we recover a number of general ergodic theorems. We then analyze some specific examples, and, in particular, give a refinement of our theory in the i.i.d. case. |
| title | Reducibility Theory and Ergodic Theorems for Ergodic Quantum Processes |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2406.10982 |