# On the geometry of mixed states and the Fisher information tensor

@article{Contreras2014OnTG, title={On the geometry of mixed states and the Fisher information tensor}, author={Iv{\'a}n A. Contreras and Elisa Ercolessi and Michele Schiavina}, journal={arXiv: Mathematical Physics}, year={2014} }

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to…

## 9 Citations

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We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible K\"ahler structure. The case of the unitary group allows us to reformulate the geometric…

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In classical information geometry one can use a potential function to generate a metric tensor and a dual pair of connections on the space of probability distributions. In a previous work, some of…

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We compare the roles of the Bures–Helstrom (BH) and Bogoliubov–Kubo–Mori (BKM) metrics in the subject of quantum information geometry. We note that there are two limits involved in state…

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In the contest of open quantum systems, we study a class of Kraus operators whose definition relies on the defining representation of the symmetric groups. We analyze the induced orbits as well as…

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The rich background of quantum-limited local estimation theory of multiple parameters that underlies these advances is reviewed and some of the main results in the field are discussed.

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A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

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(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p…

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