# A von Neumann algebra approach to quantum metrics

@article{Kuperberg2010AVN, title={A von Neumann algebra approach to quantum metrics}, author={Greg Kuperberg and Nik Weaver}, journal={arXiv: Operator Algebras}, year={2010} }

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.

## 36 Citations

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We show that any quantum family of quantum maps from a noncommutative space to a compact quantum metric space has a canonical quantum pseudo-metric structure. Here by a 'compact quantum metric space'…

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We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries…

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