dorsal/arxiv
View SchemaOrbits of quantum states and geometry of Bloch vectors for $N$-level systems
| Authors | S. G. Schirmer, T. Zhang, J. V. Leahy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0308004 |
| URL | https://arxiv.org/abs/quant-ph/0308004 |
| DOI | 10.1088/0305-4470/37/4/022 |
| Journal | J. Phys. A 37(4), 1389-1402 (2004) |
Abstract
Physical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than two. To shed some light on the complicated structure of the set of quantum states, we consider a stratification with strata given by unitary orbit manifolds, which can be identified with flag manifolds. The results are applied to study the geometry of the coherence vector for n-level quantum systems. It is shown that the unitary orbits can be naturally identified with spheres in R^{n^2-1} only for n=2. In higher dimensions the coherence vector only defines a non-surjective embedding into a closed ball. A detailed analysis of the three-level case is presented. Finally, a refined stratification in terms of symplectic orbits is considered.
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"abstract": "Physical constraints such as positivity endow the set of quantum states with\na rich geometry if the system dimension is greater than two. To shed some light\non the complicated structure of the set of quantum states, we consider a\nstratification with strata given by unitary orbit manifolds, which can be\nidentified with flag manifolds. The results are applied to study the geometry\nof the coherence vector for n-level quantum systems. It is shown that the\nunitary orbits can be naturally identified with spheres in R^{n^2-1} only for\nn=2. In higher dimensions the coherence vector only defines a non-surjective\nembedding into a closed ball. A detailed analysis of the three-level case is\npresented. Finally, a refined stratification in terms of symplectic orbits is\nconsidered.",
"arxiv_id": "quant-ph/0308004",
"authors": [
"S. G. Schirmer",
"T. Zhang",
"J. V. Leahy"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/37/4/022",
"journal_ref": "J. Phys. A 37(4), 1389-1402 (2004)",
"title": "Orbits of quantum states and geometry of Bloch vectors for $N$-level systems",
"url": "https://arxiv.org/abs/quant-ph/0308004"
},
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