A von Neumann algebra approach to quantum metrics

Details A von Neumann algebra approach to quantum metrics A von Neumann algebra approach to quantum metrics

2010-05-03

arxiv.org/abs/1005.0353v2

Mathematics

Operator Algebras

68 pages; minor revisions

Scientific paper

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.

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