Towards establishing a connection between two-level quantum systems and physical spaces
| Autor: | Valle, V. G., Brugger, L. L., Rizzuti, B. F., Duarte, Cristhiano |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Brazilian Journal of Physics 54, 93 (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s13538-024-01462-6 |
| Popis: | This work seeks to make explicit the operational connection between the preparation of two-level quantum systems with their corresponding description (as states) in a Hilbert space. This may sound outdated, but we show there is more to this connection than common sense may lead us to believe. To bridge these two separated realms -- the actual laboratory and the space of states -- we rely on a paradigmatic mathematical object: the Hopf fibration. We illustrate how this connection works in practice with a simple optical setup. Remarkably, this optical setup also reflects the necessity of using two charts to cover a sphere. Put another way, our experimental realization reflects the bi-dimensionality of a sphere seen as a smooth manifold. Comment: 10 pages, 2 figures, minor adjustments and a section added according to reviewer's suggestions |
| Databáze: | arXiv |
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