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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.27907 |
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| _version_ | 1866916066080325632 |
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| author | Huang, Yu-Huan Hou, Xu-Yang Guo, Hao Chien, Chih-Chun |
| author_facet | Huang, Yu-Huan Hou, Xu-Yang Guo, Hao Chien, Chih-Chun |
| contents | We elucidate the Bures metric in quantum state space near a rank-changing point of the density matrix and show contrasting behavior for two-level ($N=2$) systems versus higher-level systems. Due to the smooth pure-state boundary for $N=2$, we prove the apparent metric divergences to be merely coordinate artifacts and present three Lindblad processes exhibiting qualitatively different evolution near rank-changing points, showing geodesic approach, power-law scaling, and pure-state escape law. For higher-dimensional ($N\ge 3$) systems, the geometry near a rank-changing point differs fundamentally. Under suitable restrictions of the density matrix and its approach towards a pure state, the Bures metric reduces to a conical metric with the pure state at the cone tip. Such a conic geometry leads to genuine curvature singularities: A two-dimensional cone exhibits a Dirac delta-function curvature near the tip while a higher-dimensional cone shows a power-law divergence of the curvature towards the cone tip. A construction of Lindblad evolution for $N=3$ systems with conic singularities is presented, along with possible implications for future experimental and theoretical research. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27907 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry near rank-changing points on the mixed-state manifold: Bures metric, conical singularities, and Lindblad dynamics Huang, Yu-Huan Hou, Xu-Yang Guo, Hao Chien, Chih-Chun Quantum Physics Statistical Mechanics We elucidate the Bures metric in quantum state space near a rank-changing point of the density matrix and show contrasting behavior for two-level ($N=2$) systems versus higher-level systems. Due to the smooth pure-state boundary for $N=2$, we prove the apparent metric divergences to be merely coordinate artifacts and present three Lindblad processes exhibiting qualitatively different evolution near rank-changing points, showing geodesic approach, power-law scaling, and pure-state escape law. For higher-dimensional ($N\ge 3$) systems, the geometry near a rank-changing point differs fundamentally. Under suitable restrictions of the density matrix and its approach towards a pure state, the Bures metric reduces to a conical metric with the pure state at the cone tip. Such a conic geometry leads to genuine curvature singularities: A two-dimensional cone exhibits a Dirac delta-function curvature near the tip while a higher-dimensional cone shows a power-law divergence of the curvature towards the cone tip. A construction of Lindblad evolution for $N=3$ systems with conic singularities is presented, along with possible implications for future experimental and theoretical research. |
| title | Geometry near rank-changing points on the mixed-state manifold: Bures metric, conical singularities, and Lindblad dynamics |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2605.27907 |