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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.11920 |
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| _version_ | 1866908518625312768 |
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| author | Castillo, Adán Pineda, Carlos Navarrete, Erick Sebastían Davalos, David |
| author_facet | Castillo, Adán Pineda, Carlos Navarrete, Erick Sebastían Davalos, David |
| contents | Starting from a coarse-grained map of a quantum many-body system, we construct the inverse map that assigns a microscopic state to a coarse-grained state based on the maximum entropy principle. Assuming unitary evolution in the microscopic system, we examine the resulting dynamics in the coarse-grained system using the assignment map. We investigate both a two-qubit system, with \swap\ and controlled-\textsc{not}\ gates, and $n$-qubit systems, configured either in an Ising spin chain or with all-to-all interactions. We demonstrate that these dynamics exhibit atypical quantum behavior, such as nonlinearity and non-Markovianity. Furthermore, we find that these dynamics depend on the initial coarse-grained state and establish conditions for general microscopic dynamics under which linearity is preserved. As the effective dynamics induced by our coarse-grained description of many-body quantum systems diverge from conventional quantum behavior, we anticipate that this approach could aid in describing the quantum-to-classical transition and provide deeper insights into the effects of coarse graining on quantum systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11920 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coarse-grained dynamics in quantum many-body systems using the maximum entropy principle Castillo, Adán Pineda, Carlos Navarrete, Erick Sebastían Davalos, David Quantum Physics Starting from a coarse-grained map of a quantum many-body system, we construct the inverse map that assigns a microscopic state to a coarse-grained state based on the maximum entropy principle. Assuming unitary evolution in the microscopic system, we examine the resulting dynamics in the coarse-grained system using the assignment map. We investigate both a two-qubit system, with \swap\ and controlled-\textsc{not}\ gates, and $n$-qubit systems, configured either in an Ising spin chain or with all-to-all interactions. We demonstrate that these dynamics exhibit atypical quantum behavior, such as nonlinearity and non-Markovianity. Furthermore, we find that these dynamics depend on the initial coarse-grained state and establish conditions for general microscopic dynamics under which linearity is preserved. As the effective dynamics induced by our coarse-grained description of many-body quantum systems diverge from conventional quantum behavior, we anticipate that this approach could aid in describing the quantum-to-classical transition and provide deeper insights into the effects of coarse graining on quantum systems. |
| title | Coarse-grained dynamics in quantum many-body systems using the maximum entropy principle |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2407.11920 |