Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Covariance and Fisher information in quantum mechanics   Variance and Fisher information are ingredients of the Cramer-Rao inequality.
We regard Fisher information as a Riemannian metric on a quantum statistical
manifold and choose monotonicity under coarse graining as the fundamental
property of variance and Fisher information. In this approach we show that
there is a kind of dual one-to-one correspondence between the candidates of the
two concepts. We emphasis that Fisher informations are obtained from relative
entropies as contrast functions on the state space and argue that the scalar
curvature might be interpreted as an uncertainty density on a statistical
manifold.

4
The categories of this paper are: cond-mat
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The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph