Decoherence-free algebras in quantum dynamics
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909142603530240 |
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| author | Amato, Daniele Facchi, Paolo Konderak, Arturo |
| author_facet | Amato, Daniele Facchi, Paolo Konderak, Arturo |
| contents | In this Article we analyze the algebraic properties of the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. In particular, a natural product (Choi-Effros product) can be defined in the asymptotic regime. Motivated by this structure, we introduce a new space called the Choi-Effros decoherence-free algebra. Interestingly, this space is both a C* -algebra with respect to the composition product, and a B* -algebra with respect to the Choi-Effros product. Moreover, such space admits a direct-sum decomposition revealing a clear relationship with the attractor subspace of the dynamics. In particular, the equality between the attractor subspace and the Choi-Effros decoherence-free algebra is a necessary and sufficient condition for a faithful dynamics. Finally, we show how all the findings do not rely on complete positivity but on the much weaker Schwarz property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decoherence-free algebras in quantum dynamics Amato, Daniele Facchi, Paolo Konderak, Arturo Quantum Physics Mathematical Physics In this Article we analyze the algebraic properties of the asymptotic dynamics of finite-dimensional open quantum systems in the Heisenberg picture. In particular, a natural product (Choi-Effros product) can be defined in the asymptotic regime. Motivated by this structure, we introduce a new space called the Choi-Effros decoherence-free algebra. Interestingly, this space is both a C* -algebra with respect to the composition product, and a B* -algebra with respect to the Choi-Effros product. Moreover, such space admits a direct-sum decomposition revealing a clear relationship with the attractor subspace of the dynamics. In particular, the equality between the attractor subspace and the Choi-Effros decoherence-free algebra is a necessary and sufficient condition for a faithful dynamics. Finally, we show how all the findings do not rely on complete positivity but on the much weaker Schwarz property. |
| title | Decoherence-free algebras in quantum dynamics |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2403.12926 |