Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2508.16691 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908683290542080 |
|---|---|
| author | Valle, V. G. Rizzuti, B. F. |
| author_facet | Valle, V. G. Rizzuti, B. F. |
| contents | We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between vectors in three-dimensional physical space and quantum states of two-level systems, we investigate how reversible transformations-modeled as completely positive and trace-preserving maps-give rise to a correspondence between spatial rotations and unitary operations. Our approach reveals how this group-theoretic structure naturally emerges from physical constraints, particularly the preservation of purity and reversibility in quantum processes. Beyond its theoretical relevance, the construction offers a pedagogically accessible framework for introducing core ideas in quantum mechanics and symmetry groups, making the abstract correspondence between $SU(2)$ and $SO(3)$ tangible through experimentally meaningful procedures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16691 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Rotations to Unitaries: Reversible Quantum Processes and the Emergence of the $SU(2)-SO(3)$ Homomorphism Valle, V. G. Rizzuti, B. F. Quantum Physics 81P16 We present an operational reconstruction of the well-known two-to-one homomorphism between the groups $SU(2)$ and $SO(3)$, grounded in the physical description of quantum state preparation and evolution. Starting from the connection between vectors in three-dimensional physical space and quantum states of two-level systems, we investigate how reversible transformations-modeled as completely positive and trace-preserving maps-give rise to a correspondence between spatial rotations and unitary operations. Our approach reveals how this group-theoretic structure naturally emerges from physical constraints, particularly the preservation of purity and reversibility in quantum processes. Beyond its theoretical relevance, the construction offers a pedagogically accessible framework for introducing core ideas in quantum mechanics and symmetry groups, making the abstract correspondence between $SU(2)$ and $SO(3)$ tangible through experimentally meaningful procedures. |
| title | From Rotations to Unitaries: Reversible Quantum Processes and the Emergence of the $SU(2)-SO(3)$ Homomorphism |
| topic | Quantum Physics 81P16 |
| url | https://arxiv.org/abs/2508.16691 |