Geometric phase for SU(N) through fiber bundles and unitary integration
| dc.creator | Uskov, D. B. | |
| dc.creator | Rau, A. R. P. | |
| dc.date | 2005-11-19 | |
| dc.date | 2006-05-24 | |
| dc.date.accessioned | 2026-07-07T11:36:47Z | |
| dc.date.available | 2026-07-07T11:36:47Z | |
| dc.description | Geometric phases are important in quantum physics and now central to fault tolerant quantum computation. For spin-1/2 and SU(2), the Bloch sphere $S^2$, together with a U(1) phase, provides a complete SU(2) description. We generalize to $N$-level systems and SU($N$) in terms of a $2(N-1)$-dimensional base space and reduction to a ($N$-1)-level problem, paralleling closely the two-dimensional case. This iteratively solves the time evolution of an $N$-level system and gives ($N$-1) geometric phases explicitly. A complete analytical construction of a S^4 Bloch-like sphere for two qubits is given for the Spin(5) or SO(5) subgroup of SU(4). | |
| dc.description | 4 pages. Following referee reports in April 2006, stylistic changes made throughout and a specific application added at the end | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0511192 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0511192 | |
| dc.identifier | Phys.Rev.A74:030304,2006 | |
| dc.identifier | doi:10.1103/PhysRevA.74.030304 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/199040 | |
| dc.subject | Quantum Physics | |
| dc.title | Geometric phase for SU(N) through fiber bundles and unitary integration | |
| dc.type | text |