Provably Time-Optimal Cooling of Markovian Quantum Systems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909132544540672 |
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| author | Malvetti, Emanuel |
| author_facet | Malvetti, Emanuel |
| contents | We address the problem of cooling a Markovian quantum system to a pure state in the shortest amount of time possible. Here the system drift takes the form of a Lindblad master equation and we assume fast unitary control. This setting allows for a natural reduction of the control system to the eigenvalues of the state density matrix. We give a simple necessary and sufficient characterization of systems which are (asymptotically) coolable and present a powerful result which allows to considerably simplify the search for optimal cooling solutions. With these tools at our disposal we derive explicit provably time-optimal cooling protocols for rank one qubit systems, inverted $Λ$-systems on a qutrit, and a certain system consisting of two coupled qubits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Provably Time-Optimal Cooling of Markovian Quantum Systems Malvetti, Emanuel Quantum Physics Optimization and Control 81Q93 (Primary) 49J24, 49K24, 15A18, 37N20, 15A51 (Secondary) We address the problem of cooling a Markovian quantum system to a pure state in the shortest amount of time possible. Here the system drift takes the form of a Lindblad master equation and we assume fast unitary control. This setting allows for a natural reduction of the control system to the eigenvalues of the state density matrix. We give a simple necessary and sufficient characterization of systems which are (asymptotically) coolable and present a powerful result which allows to considerably simplify the search for optimal cooling solutions. With these tools at our disposal we derive explicit provably time-optimal cooling protocols for rank one qubit systems, inverted $Λ$-systems on a qutrit, and a certain system consisting of two coupled qubits. |
| title | Provably Time-Optimal Cooling of Markovian Quantum Systems |
| topic | Quantum Physics Optimization and Control 81Q93 (Primary) 49J24, 49K24, 15A18, 37N20, 15A51 (Secondary) |
| url | https://arxiv.org/abs/2403.05285 |