A Comparison of Two Quantum Distances

Jens Kaad; David Kyed

doi:10.1007/s11040-023-09451-y

A Comparison of Two Quantum Distances

Jens Kaad, David Kyed^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › Research › peer-review

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Abstract

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 language	English
Article number	8
Journal	Mathematical Physics, Analysis and Geometry
Volume	26
Issue number	1
Number of pages	9
ISSN	1385-0172
DOIs	https://doi.org/10.1007/s11040-023-09451-y
Publication status	Published - 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.

Keywords

Gromov–Hausdorff distance
Quantum metric spaces
State spaces

Documents & Links

10.1007/s11040-023-09451-y

Open Access VersionAccepted manuscript, 301 KB

Cite this

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title = "A Comparison of Two Quantum Distances",

abstract = "We show that Rieffel{\textquoteright}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.",

keywords = "Gromov–Hausdorff distance, Quantum metric spaces, State spaces",

author = "Jens Kaad and David Kyed",

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.",

year = "2023",

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AU - Kaad, Jens

AU - Kyed, David

N1 - 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.

PY - 2023/3

Y1 - 2023/3

N2 - 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.

AB - 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.

KW - Gromov–Hausdorff distance

KW - Quantum metric spaces

KW - State spaces

U2 - 10.1007/s11040-023-09451-y

DO - 10.1007/s11040-023-09451-y

M3 - Journal article

AN - SCOPUS:85150498188

SN - 1385-0172

VL - 26

JO - Mathematical Physics, Analysis and Geometry

JF - Mathematical Physics, Analysis and Geometry

IS - 1

M1 - 8

ER -

A Comparison of Two Quantum Distances

Abstract

Bibliographical note

Keywords

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Cite this