A Comparison of Two Quantum Distances

Jens Kaad, David Kyed*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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.

Original languageEnglish
Article number8
JournalMathematical Physics, Analysis and Geometry
Issue number1
Number of pages9
Publication statusPublished - Mar 2023

Bibliographical note

Funding 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


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