Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of mixed states for a q-bit and the quantum Fisher information
  tensor   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, whose base space can be identified with a co-adjoint orbit of
the unitary group. We show that the Fisher Information metric coincides with
the one induced by the metric of the manifold of SU(2), i.e. the 3-dimensional
sphere $S^3$, when the mixing coefficients are varied. We define the notion of
Fisher Tensor and show that its anti-symmetric part is intrinsically related to
the Kostant Kirillov Souriau symplectic form that is naturally defined on
co-adjoint orbits, while the symmetric part is nontrivially again represented
by the Fubini Study metric on the space of mixed states, weighted by the mixing
coefficients.

36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics