Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A von Neumann algebra approach to quantum metrics   We propose a new definition of quantum metric spaces, or W*-metric spaces, in
the setting of von Neumann algebras. Our definition effectively reduces to the
classical notion in the atomic abelian case, has both concrete and intrinsic
characterizations, and admits a wide variety of tractable examples. A natural
application and motivation of our theory is a mutual generalization of the
standard models of classical and quantum error correction.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg