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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2404.15179 |
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| _version_ | 1866916219717681152 |
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| author | Morelli, Simon Llorens, Santiago Siewert, Jens |
| author_facet | Morelli, Simon Llorens, Santiago Siewert, Jens |
| contents | The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is intuitively clear that some of the imaginary coordinates cannot have the same extension as their real counterparts the precise relation is not obvious. We give a complete characterization of the constraints in terms of tight inequalities for real and imaginary Bloch-type coordinates. Our description entails a three-dimensional Bloch ball-type model for the state space. We uncover a surprising qualitative difference for the state-space boundaries in even and odd dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15179 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring Imaginary Coordinates: Disparity in the Shape of Quantum State Space in Even and Odd Dimensions Morelli, Simon Llorens, Santiago Siewert, Jens Quantum Physics The state of a finite-dimensional quantum system is described by a density matrix that can be decomposed into a real diagonal, a real off-diagonal and and an imaginary off-diagonal part. The latter plays a peculiar role. While it is intuitively clear that some of the imaginary coordinates cannot have the same extension as their real counterparts the precise relation is not obvious. We give a complete characterization of the constraints in terms of tight inequalities for real and imaginary Bloch-type coordinates. Our description entails a three-dimensional Bloch ball-type model for the state space. We uncover a surprising qualitative difference for the state-space boundaries in even and odd dimensions. |
| title | Exploring Imaginary Coordinates: Disparity in the Shape of Quantum State Space in Even and Odd Dimensions |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2404.15179 |