A von Neumann algebra approach to quantum metrics
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2010
- DOI:
- 10.48550/arXiv.1005.0353
- arXiv:
- arXiv:1005.0353
- Bibcode:
- 2010arXiv1005.0353K
- Keywords:
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- Mathematics - Operator Algebras;
- Quantum Physics
- E-Print:
- 68 pages