Characterizing Optimal-speed unitary time evolution of pure and quasi-pure quantum states
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910566092636160 |
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| author | Rodríguez, John A. Mora Grajales, Brian Cunha, Marcelo Terra Grama, Lino |
| author_facet | Rodríguez, John A. Mora Grajales, Brian Cunha, Marcelo Terra Grama, Lino |
| contents | We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_07794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing Optimal-speed unitary time evolution of pure and quasi-pure quantum states Rodríguez, John A. Mora Grajales, Brian Cunha, Marcelo Terra Grama, Lino Quantum Physics Mathematical Physics Differential Geometry 81R99, 53C30 We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states. |
| title | Characterizing Optimal-speed unitary time evolution of pure and quasi-pure quantum states |
| topic | Quantum Physics Mathematical Physics Differential Geometry 81R99, 53C30 |
| url | https://arxiv.org/abs/2408.07794 |