---
_id: '12087'
abstract:
- lang: eng
  text: Following up on the recent work on lower Ricci curvature bounds for quantum
    systems, we introduce two noncommutative versions of curvature-dimension bounds
    for symmetric quantum Markov semigroups over matrix algebras. Under suitable such
    curvature-dimension conditions, we prove a family of dimension-dependent functional
    inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power
    in the noncommutative setting. We also provide examples satisfying certain curvature-dimension
    conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers
    over group algebras and generalized depolarizing semigroups.
acknowledgement: H.Z. is supported by the European Union’s Horizon 2020 research and
  innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411
  and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges
  support from the European Research Council (ERC) under the European Union’s Horizon
  2020 research and innovation programme (Grant Agreement No. 716117) and from the
  Austrian Science Fund (FWF) through grant number F65. Both authors would like to
  thank Jan Maas for fruitful discussions and helpful comments. Open access funding
  provided by Austrian Science Fund (FWF).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Melchior
  full_name: Wirth, Melchior
  id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
  last_name: Wirth
  orcid: 0000-0002-0519-4241
- first_name: Haonan
  full_name: Zhang, Haonan
  id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
  last_name: Zhang
citation:
  ama: Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov
    semigroups. <i>Annales Henri Poincare</i>. 2023;24:717-750. doi:<a href="https://doi.org/10.1007/s00023-022-01220-x">10.1007/s00023-022-01220-x</a>
  apa: Wirth, M., &#38; Zhang, H. (2023). Curvature-dimension conditions for symmetric
    quantum Markov semigroups. <i>Annales Henri Poincare</i>. Springer Nature. <a
    href="https://doi.org/10.1007/s00023-022-01220-x">https://doi.org/10.1007/s00023-022-01220-x</a>
  chicago: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for
    Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>. Springer
    Nature, 2023. <a href="https://doi.org/10.1007/s00023-022-01220-x">https://doi.org/10.1007/s00023-022-01220-x</a>.
  ieee: M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum
    Markov semigroups,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp.
    717–750, 2023.
  ista: Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum
    Markov semigroups. Annales Henri Poincare. 24, 717–750.
  mla: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric
    Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature,
    2023, pp. 717–50, doi:<a href="https://doi.org/10.1007/s00023-022-01220-x">10.1007/s00023-022-01220-x</a>.
  short: M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.
corr_author: '1'
date_created: 2022-09-11T22:01:57Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2025-04-23T08:53:05Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00023-022-01220-x
ec_funded: 1
external_id:
  arxiv:
  - '2105.08303'
  isi:
  - '000837499800002'
  pmid:
  - '36950223'
file:
- access_level: open_access
  checksum: 8c7b185eba5ccd92ef55c120f654222c
  content_type: application/pdf
  creator: dernst
  date_created: 2023-08-14T11:38:28Z
  date_updated: 2023-08-14T11:38:28Z
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  file_name: 2023_AnnalesHenriPoincare_Wirth.pdf
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file_date_updated: 2023-08-14T11:38:28Z
fulldoi: https://doi.org/10.1007/s00023-022-01220-x
has_accepted_license: '1'
intvolume: '        24'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '03'
oa: 1
oa_version: Published Version
page: 717-750
pmid: 1
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
  grant_number: M03337
  name: Curvature-dimension in noncommutative analysis
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
publication: Annales Henri Poincare
publication_identifier:
  issn:
  - 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Curvature-dimension conditions for symmetric quantum Markov semigroups
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...