A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909900843515904 |
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| author | Ekblad, Owen |
| author_facet | Ekblad, Owen |
| contents | We prove a multiplicative ergodic theorem for bistochastic completely positive (bcp) linear cocycles acting on finite-dimensional matrix algebras, giving an invariant splitting described explicitly in terms of the multiplicative domains of the underlying bcp maps. As an application of our theorem, we classify when compositions of random bcp maps are asymptotically entanglement breaking, and use this classification to show that occasionally PPT bcp maps are asymptotically entanglement breaking. We conclude by demonstrating a certain class of bcp linear cocycles are almost surely entanglement breaking in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement Ekblad, Owen Quantum Physics Mathematical Physics Dynamical Systems 81P42, 81S22, 81R15, 37H15 We prove a multiplicative ergodic theorem for bistochastic completely positive (bcp) linear cocycles acting on finite-dimensional matrix algebras, giving an invariant splitting described explicitly in terms of the multiplicative domains of the underlying bcp maps. As an application of our theorem, we classify when compositions of random bcp maps are asymptotically entanglement breaking, and use this classification to show that occasionally PPT bcp maps are asymptotically entanglement breaking. We conclude by demonstrating a certain class of bcp linear cocycles are almost surely entanglement breaking in finite time. |
| title | A Multiplicative Ergodic Theorem for Bistochastic Ergodic Quantum Processes with Applications to Entanglement |
| topic | Quantum Physics Mathematical Physics Dynamical Systems 81P42, 81S22, 81R15, 37H15 |
| url | https://arxiv.org/abs/2502.14997 |