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Canonical coset parametrization and the Bures metric of the three-level quantum systems. (English) Zbl 1121.81059
Summary: An explicit parametrization for the state space of an \(n\)-level density matrix is given. The parametrization is based on the canonical coset decomposition of unitary matrices. We also compute, explicitly, the Bures metric tensor over the state space of two- and three-level quantum systems.

MSC:
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
15A90 Applications of matrix theory to physics (MSC2000)
20C35 Applications of group representations to physics and other areas of science
81P15 Quantum measurement theory, state operations, state preparations
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
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