We show that Rieffel’s quantum Gromov–Hausdorff distance between two compact quantum metric spaces is not equivalent to the ordinary Gromov–Hausdorff distance applied to the associated state spaces.
Bibliographical noteFunding Information:
The authors gratefully acknowledge the financial support from the Independent Research Fund Denmark through Grant Nos. 9040-00107B, 7014-00145B and 1026-00371B.
- Gromov–Hausdorff distance
- Quantum metric spaces
- State spaces