dorsal/arxiv
View SchemaThe Bloch-vector space for N-level systems -- the spherical-coordinate point of view
| Authors | Gen Kimura, Andrzej Kossakowski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0408014 |
| URL | https://arxiv.org/abs/quant-ph/0408014 |
| Journal | Open Sys. Information Dyn. 12, 207 (2005). |
Abstract
Bloch-vector spaces for $N$-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We show that the maximum radius in each direction, which is due to the construction of the Bloch-vector space, is determined by the minimum eigenvalue of the corresponding observable (orthogonal generator of SU(N)). From this fact, we reveal the dual property of the structure of the Bloch-vector space; if in some direction the space reachs the large sphere (pure state), then in the opposite direction the space can only get to the small sphere, and vice versa. Another application is a parameterization with simple ranges of density operators. We also provide three classes of quantum-state representation based on actual measurements beyond the Bloch vector and discuss their state-spaces.
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"abstract": "Bloch-vector spaces for $N$-level systems are investigated from the\nspherical-coordinate point of view in order to understand their geometrical\naspects. We show that the maximum radius in each direction, which is due to the\nconstruction of the Bloch-vector space, is determined by the minimum eigenvalue\nof the corresponding observable (orthogonal generator of SU(N)). From this\nfact, we reveal the dual property of the structure of the Bloch-vector space;\nif in some direction the space reachs the large sphere (pure state), then in\nthe opposite direction the space can only get to the small sphere, and vice\nversa. Another application is a parameterization with simple ranges of density\noperators. We also provide three classes of quantum-state representation based\non actual measurements beyond the Bloch vector and discuss their state-spaces.",
"arxiv_id": "quant-ph/0408014",
"authors": [
"Gen Kimura",
"Andrzej Kossakowski"
],
"categories": [
"quant-ph"
],
"journal_ref": "Open Sys. Information Dyn. 12, 207 (2005).",
"title": "The Bloch-vector space for N-level systems -- the spherical-coordinate point of view",
"url": "https://arxiv.org/abs/quant-ph/0408014"
},
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