Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of quantum evolution for mixed quantum states   The geometric formulation of quantum mechanics is a very interesting field of
research which has many applications in the emerging field of quantum
computation and quantum information, such as schemes for optimal quantum
computers. In this work we discuss a geometric formulation of mixed quantum
states represented by density operators. Our formulation is based on principal
fiber bundles and purifications of quantum states. In our construction, the
Riemannian metric and symplectic form on the total space are induced from the
real and imaginary parts of the Hilbert-Schmidt Hermitian inner product, and we
define a mechanical connection in terms of a locked inertia tensor and moment
map. We also discuss some applications of our geometric framework.

25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th