2003/08/31 by S. G. Schirmer, T. Zhang, T Zhang +2 · 1 citation
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.1088/0305-4470/37/4/022
published as J. Phys. A 37(4), 1389-1402 (2004) · 15 pages LaTeX, 3 figures, reformatted, slightly modified version, corrected eq.(3), to appear in J. Physics A
arxiv created 2003/11/26 · openalex publication_date 2004/01/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Physical 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.