E. Ercolessi, M. Schiavina
After a review of the pure state case, we discuss from a geometrical point of view the meaning of the Quantum Fisher metric in the case of mixed states for a two-level system, i.e. for a q-bit, by examining the structure of the fiber bundle of states, which can also be identified with a co-adjoint orbit of the unitary group. We show that the full quantum Fisher tensor has a symmetric part that coincides with the metric of the manifold of SU(2), i.e. the 3-dimensional sphere $S^3$, and an anti-symmetric part that is intrinsically related to the KKS-symplectic form that is naturally defined on co-adjoint orbits.
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http://arxiv.org/abs/1205.2561
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