S G Schirmer et al 2004 J. Phys. A: Math. Gen. 37 1389 doi:10.1088/0305-4470/37/4/022
Orbits of quantum states and geometry of Bloch vectors for N-level systems
S G Schirmer1,2, T Zhang3 and J V Leahy4
Show affiliationsPhysical constraints such as positivity endow the set of quantum states with a rich geometry if the system dimension is greater than 2. 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 
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.
- PACS
- MSC
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81R30 Coherent states (See also 22E45); squeezed states (See also 81V80)
81S10 Geometry and quantization, symplectic methods (See also 53D50)
- Subjects
- Dates
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Issue 4 (30 January 2004)
Received 4 August 2003, in final form 15 October 2003
Published 9 January 2004
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Orbits of quantum states and geometry of Bloch vectors for N-level systems
S G Schirmer et al 2004 J. Phys. A: Math. Gen. 37 1389
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