---
_id: '13226'
abstract:
- lang: eng
  text: We consider the ground state and the low-energy excited states of a system
    of N identical bosons with interactions in the mean-field scaling regime. For
    the ground state, we derive a weak Edgeworth expansion for the fluctuations of
    bounded one-body operators, which yields corrections to a central limit theorem
    to any order in 1/N−−√. For suitable excited states, we show that the limiting
    distribution is a polynomial times a normal distribution, and that higher-order
    corrections are given by an Edgeworth-type expansion.
acknowledgement: "It is a pleasure to thank Martin Kolb, Simone Rademacher, Robert
  Seiringer and Stefan Teufel for helpful discussions. Moreover, we thank the referee
  for many constructive comments. L.B. gratefully acknowledges funding from the German
  Research Foundation within the Munich Center of Quantum Science and Technology (EXC
  2111) and from the European Union’s Horizon 2020 research and innovation programme
  under the Marie Skłodowska-Curie Grant Agreement No. 754411. We thank the Mathematical
  Research Institute Oberwolfach, where part of this work was done, for their hospitality.\r\nOpen
  Access funding enabled and organized by Projekt DEAL."
article_number: '77'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Lea
  full_name: Bossmann, Lea
  id: A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425
  last_name: Bossmann
  orcid: 0000-0002-6854-1343
- first_name: Sören P
  full_name: Petrat, Sören P
  id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrat
  orcid: 0000-0002-9166-5889
citation:
  ama: Bossmann L, Petrat SP. Weak Edgeworth expansion for the mean-field Bose gas.
    <i>Letters in Mathematical Physics</i>. 2023;113(4). doi:<a href="https://doi.org/10.1007/s11005-023-01698-4">10.1007/s11005-023-01698-4</a>
  apa: Bossmann, L., &#38; Petrat, S. P. (2023). Weak Edgeworth expansion for the
    mean-field Bose gas. <i>Letters in Mathematical Physics</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s11005-023-01698-4">https://doi.org/10.1007/s11005-023-01698-4</a>
  chicago: Bossmann, Lea, and Sören P Petrat. “Weak Edgeworth Expansion for the Mean-Field
    Bose Gas.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2023. <a href="https://doi.org/10.1007/s11005-023-01698-4">https://doi.org/10.1007/s11005-023-01698-4</a>.
  ieee: L. Bossmann and S. P. Petrat, “Weak Edgeworth expansion for the mean-field
    Bose gas,” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4. Springer Nature,
    2023.
  ista: Bossmann L, Petrat SP. 2023. Weak Edgeworth expansion for the mean-field Bose
    gas. Letters in Mathematical Physics. 113(4), 77.
  mla: Bossmann, Lea, and Sören P. Petrat. “Weak Edgeworth Expansion for the Mean-Field
    Bose Gas.” <i>Letters in Mathematical Physics</i>, vol. 113, no. 4, 77, Springer
    Nature, 2023, doi:<a href="https://doi.org/10.1007/s11005-023-01698-4">10.1007/s11005-023-01698-4</a>.
  short: L. Bossmann, S.P. Petrat, Letters in Mathematical Physics 113 (2023).
date_created: 2023-07-16T22:01:08Z
date_published: 2023-07-03T00:00:00Z
date_updated: 2023-12-13T11:31:50Z
day: '03'
department:
- _id: RoSe
doi: 10.1007/s11005-023-01698-4
ec_funded: 1
external_id:
  arxiv:
  - '2208.00199'
  isi:
  - '001022878900002'
intvolume: '       113'
isi: 1
issue: '4'
language:
- iso: eng
month: '07'
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weak Edgeworth expansion for the mean-field Bose gas
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 113
year: '2023'
...
---
_id: '10642'
abstract:
- lang: eng
  text: Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized
    but otherwise arbitrary perturbations of weakly interacting quantum spin systems
    with uniformly gapped on-site terms change the ground state of such a system only
    locally, even if they close the spectral gap. We call this a strong version of
    the local perturbations perturb locally (LPPL) principle which is known to hold
    for much more general gapped systems, but only for perturbations that do not close
    the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle
    to Hamiltonians that have the appropriate structure of gapped on-site terms and
    weak interactions only locally in some region of space. While our results are
    technically corollaries to a theorem of Yarotsky, we expect that the paradigm
    of systems with a locally gapped ground state that is completely insensitive to
    the form of the Hamiltonian elsewhere extends to other situations and has important
    physical consequences.
acknowledgement: J. H. acknowledges partial financial support by the ERC Advanced
  Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for
  very helpful comments and discussions and Jürg Fröhlich for references to the literature.
  Open Access funding enabled and organized by Projekt DEAL.
article_number: '9'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Stefan
  full_name: Teufel, Stefan
  last_name: Teufel
- first_name: Tom
  full_name: Wessel, Tom
  last_name: Wessel
citation:
  ama: Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally
    gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical
    Physics</i>. 2022;112(1). doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a>
  apa: Henheik, S. J., Teufel, S., &#38; Wessel, T. (2022). Local stability of ground
    states in locally gapped and weakly interacting quantum spin systems. <i>Letters
    in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a>
  chicago: Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of
    Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.”
    <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s11005-021-01494-y">https://doi.org/10.1007/s11005-021-01494-y</a>.
  ieee: S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states
    in locally gapped and weakly interacting quantum spin systems,” <i>Letters in
    Mathematical Physics</i>, vol. 112, no. 1. Springer Nature, 2022.
  ista: Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in
    locally gapped and weakly interacting quantum spin systems. Letters in Mathematical
    Physics. 112(1), 9.
  mla: Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped
    and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>,
    vol. 112, no. 1, 9, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s11005-021-01494-y">10.1007/s11005-021-01494-y</a>.
  short: S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).
date_created: 2022-01-18T16:18:25Z
date_published: 2022-01-18T00:00:00Z
date_updated: 2023-08-02T13:57:02Z
day: '18'
ddc:
- '530'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1007/s11005-021-01494-y
ec_funded: 1
external_id:
  arxiv:
  - '2106.13780'
  isi:
  - '000744930400001'
file:
- access_level: open_access
  checksum: 7e8e69b76e892c305071a4736131fe18
  content_type: application/pdf
  creator: cchlebak
  date_created: 2022-01-19T09:41:14Z
  date_updated: 2022-01-19T09:41:14Z
  file_id: '10647'
  file_name: 2022_LettersMathPhys_Henheik.pdf
  file_size: 357547
  relation: main_file
  success: 1
file_date_updated: 2022-01-19T09:41:14Z
has_accepted_license: '1'
intvolume: '       112'
isi: 1
issue: '1'
keyword:
- mathematical physics
- statistical and nonlinear physics
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Local stability of ground states in locally gapped and weakly interacting quantum
  spin systems
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 112
year: '2022'
...
---
_id: '12246'
abstract:
- lang: eng
  text: The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of
    a classical system of N identical charges only in terms of their one-particle
    density. We prove here a new estimate on the best constant in this inequality.
    Numerical evaluation provides the value 1.58, which is a significant improvement
    to the previously known value 1.64. The best constant has recently been shown
    to be larger than 1.44. In a second part, we prove that the constant can be reduced
    to 1.25 when the inequality is restricted to Hartree–Fock states. This is the
    first proof that the exchange term is always much lower than the full indirect
    Coulomb energy.
acknowledgement: We would like to thank David Gontier for useful advice on the numerical
  simulations. This project has received funding from the European Research Council
  (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant
  Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful
  for the hospitality of the Institut Henri Poincaré in Paris, where part of this
  work was done.
article_number: '92'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
  full_name: Lewin, Mathieu
  last_name: Lewin
- first_name: Elliott H.
  full_name: Lieb, Elliott H.
  last_name: Lieb
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and
    exchange energies. <i>Letters in Mathematical Physics</i>. 2022;112(5). doi:<a
    href="https://doi.org/10.1007/s11005-022-01584-5">10.1007/s11005-022-01584-5</a>
  apa: Lewin, M., Lieb, E. H., &#38; Seiringer, R. (2022). Improved Lieb–Oxford bound
    on the indirect and exchange energies. <i>Letters in Mathematical Physics</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s11005-022-01584-5">https://doi.org/10.1007/s11005-022-01584-5</a>
  chicago: Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford
    Bound on the Indirect and Exchange Energies.” <i>Letters in Mathematical Physics</i>.
    Springer Nature, 2022. <a href="https://doi.org/10.1007/s11005-022-01584-5">https://doi.org/10.1007/s11005-022-01584-5</a>.
  ieee: M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the
    indirect and exchange energies,” <i>Letters in Mathematical Physics</i>, vol.
    112, no. 5. Springer Nature, 2022.
  ista: Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect
    and exchange energies. Letters in Mathematical Physics. 112(5), 92.
  mla: Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange
    Energies.” <i>Letters in Mathematical Physics</i>, vol. 112, no. 5, 92, Springer
    Nature, 2022, doi:<a href="https://doi.org/10.1007/s11005-022-01584-5">10.1007/s11005-022-01584-5</a>.
  short: M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).
date_created: 2023-01-16T09:53:54Z
date_published: 2022-09-15T00:00:00Z
date_updated: 2023-09-05T15:17:34Z
day: '15'
department:
- _id: RoSe
doi: 10.1007/s11005-022-01584-5
ec_funded: 1
external_id:
  arxiv:
  - '2203.12473'
  isi:
  - '000854762600001'
intvolume: '       112'
isi: 1
issue: '5'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2203.12473
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Improved Lieb–Oxford bound on the indirect and exchange energies
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 112
year: '2022'
...
---
_id: '9121'
abstract:
- lang: eng
  text: "We show that the energy gap for the BCS gap equation is\r\nΞ=μ(8e−2+o(1))exp(π2μ−−√a)\r\nin
    the low density limit μ→0. Together with the similar result for the critical temperature
    by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in
    the low density limit, the ratio of the energy gap and critical temperature is
    a universal constant independent of the interaction potential V. The results hold
    for a class of potentials with negative scattering length a and no bound states."
acknowledgement: "Most of this work was done as part of the author’s master’s thesis.
  The author would like to thank Jan Philip Solovej for his supervision of this process.\r\nOpen
  Access funding provided by Institute of Science and Technology (IST Austria)"
article_number: '20'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Asbjørn Bækgaard
  full_name: Lauritsen, Asbjørn Bækgaard
  id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
  last_name: Lauritsen
  orcid: 0000-0003-4476-2288
citation:
  ama: Lauritsen AB. The BCS energy gap at low density. <i>Letters in Mathematical
    Physics</i>. 2021;111. doi:<a href="https://doi.org/10.1007/s11005-021-01358-5">10.1007/s11005-021-01358-5</a>
  apa: Lauritsen, A. B. (2021). The BCS energy gap at low density. <i>Letters in Mathematical
    Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-021-01358-5">https://doi.org/10.1007/s11005-021-01358-5</a>
  chicago: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” <i>Letters
    in Mathematical Physics</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s11005-021-01358-5">https://doi.org/10.1007/s11005-021-01358-5</a>.
  ieee: A. B. Lauritsen, “The BCS energy gap at low density,” <i>Letters in Mathematical
    Physics</i>, vol. 111. Springer Nature, 2021.
  ista: Lauritsen AB. 2021. The BCS energy gap at low density. Letters in Mathematical
    Physics. 111, 20.
  mla: Lauritsen, Asbjørn Bækgaard. “The BCS Energy Gap at Low Density.” <i>Letters
    in Mathematical Physics</i>, vol. 111, 20, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s11005-021-01358-5">10.1007/s11005-021-01358-5</a>.
  short: A.B. Lauritsen, Letters in Mathematical Physics 111 (2021).
date_created: 2021-02-15T09:27:14Z
date_published: 2021-02-12T00:00:00Z
date_updated: 2023-09-05T15:17:16Z
day: '12'
ddc:
- '510'
department:
- _id: GradSch
doi: 10.1007/s11005-021-01358-5
external_id:
  isi:
  - '000617531900001'
file:
- access_level: open_access
  checksum: eaf1b3ff5026f120f0929a5c417dc842
  content_type: application/pdf
  creator: dernst
  date_created: 2021-02-15T09:31:07Z
  date_updated: 2021-02-15T09:31:07Z
  file_id: '9122'
  file_name: 2021_LettersMathPhysics_Lauritsen.pdf
  file_size: 329332
  relation: main_file
  success: 1
file_date_updated: 2021-02-15T09:31:07Z
has_accepted_license: '1'
intvolume: '       111'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: The BCS energy gap at low density
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 111
year: '2021'
...
---
_id: '7611'
abstract:
- lang: eng
  text: We consider a system of N bosons in the limit N→∞, interacting through singular
    potentials. For initial data exhibiting Bose–Einstein condensation, the many-body
    time evolution is well approximated through a quadratic fluctuation dynamics around
    a cubic nonlinear Schrödinger equation of the condensate wave function. We show
    that these fluctuations satisfy a (multi-variate) central limit theorem.
acknowledgement: "Simone Rademacher acknowledges partial support from the NCCR SwissMAP.
  This project has received\r\nfunding from the European Union’s Horizon 2020 research
  and innovation program under the Marie\r\nSkłodowska-Curie Grant Agreement No. 754411.\r\nOpen
  access funding provided by Institute of Science and Technology (IST Austria).\r\nS.R.
  would like to thank Benjamin Schlein for many fruitful discussions."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Simone Anna Elvira
  full_name: Rademacher, Simone Anna Elvira
  id: 856966FE-A408-11E9-977E-802DE6697425
  last_name: Rademacher
  orcid: 0000-0001-5059-4466
citation:
  ama: Rademacher SAE. Central limit theorem for Bose gases interacting through singular
    potentials. <i>Letters in Mathematical Physics</i>. 2020;110:2143-2174. doi:<a
    href="https://doi.org/10.1007/s11005-020-01286-w">10.1007/s11005-020-01286-w</a>
  apa: Rademacher, S. A. E. (2020). Central limit theorem for Bose gases interacting
    through singular potentials. <i>Letters in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s11005-020-01286-w">https://doi.org/10.1007/s11005-020-01286-w</a>
  chicago: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
    through Singular Potentials.” <i>Letters in Mathematical Physics</i>. Springer
    Nature, 2020. <a href="https://doi.org/10.1007/s11005-020-01286-w">https://doi.org/10.1007/s11005-020-01286-w</a>.
  ieee: S. A. E. Rademacher, “Central limit theorem for Bose gases interacting through
    singular potentials,” <i>Letters in Mathematical Physics</i>, vol. 110. Springer
    Nature, pp. 2143–2174, 2020.
  ista: Rademacher SAE. 2020. Central limit theorem for Bose gases interacting through
    singular potentials. Letters in Mathematical Physics. 110, 2143–2174.
  mla: Rademacher, Simone Anna Elvira. “Central Limit Theorem for Bose Gases Interacting
    through Singular Potentials.” <i>Letters in Mathematical Physics</i>, vol. 110,
    Springer Nature, 2020, pp. 2143–74, doi:<a href="https://doi.org/10.1007/s11005-020-01286-w">10.1007/s11005-020-01286-w</a>.
  short: S.A.E. Rademacher, Letters in Mathematical Physics 110 (2020) 2143–2174.
date_created: 2020-03-23T11:11:47Z
date_published: 2020-03-12T00:00:00Z
date_updated: 2023-09-05T15:14:50Z
day: '12'
ddc:
- '510'
department:
- _id: RoSe
doi: 10.1007/s11005-020-01286-w
ec_funded: 1
external_id:
  isi:
  - '000551556000006'
file:
- access_level: open_access
  checksum: 3bdd41f10ad947b67a45b98f507a7d4a
  content_type: application/pdf
  creator: dernst
  date_created: 2020-11-20T12:04:26Z
  date_updated: 2020-11-20T12:04:26Z
  file_id: '8784'
  file_name: 2020_LettersMathPhysics_Rademacher.pdf
  file_size: 478683
  relation: main_file
  success: 1
file_date_updated: 2020-11-20T12:04:26Z
has_accepted_license: '1'
intvolume: '       110'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 2143-2174
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Central limit theorem for Bose gases interacting through singular potentials
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 110
year: '2020'
...
---
_id: '7618'
abstract:
- lang: eng
  text: 'This short note aims to study quantum Hellinger distances investigated recently
    by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis
    on barycenters. We introduce the family of generalized quantum Hellinger divergences
    that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando
    mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to
    the family of maximal quantum f-divergences, and hence are jointly convex, and
    satisfy the data processing inequality. We derive a characterization of the barycenter
    of finitely many positive definite operators for these generalized quantum Hellinger
    divergences. We note that the characterization of the barycenter as the weighted
    multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true
    in the case of commuting operators, but it is not correct in the general case. '
acknowledgement: "J. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum
  Grant for Quantum\r\nInformation Theory, No. 96 141, and by the Hungarian National
  Research, Development and Innovation\r\nOffice (NKFIH) via Grants Nos. K119442,
  K124152 and KH129601. D. Virosztek was supported by the\r\nISTFELLOW program of
  the Institute of Science and Technology Austria (Project Code IC1027FELL01),\r\nby
  the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSklodowska-Curie
  Grant Agreement No. 846294, and partially supported by the Hungarian National\r\nResearch,
  Development and Innovation Office (NKFIH) via Grants Nos. K124152 and KH129601.\r\nWe
  are grateful to Milán Mosonyi for drawing our attention to Ref.’s [6,14,15,17,\r\n20,21],
  for comments on earlier versions of this paper, and for several discussions on the
  topic. We are\r\nalso grateful to Miklós Pálfia for several discussions; to László
  Erdös for his essential suggestions on the\r\nstructure and highlights of this paper,
  and for his comments on earlier versions; and to the anonymous\r\nreferee for his/her
  valuable comments and suggestions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jozsef
  full_name: Pitrik, Jozsef
  last_name: Pitrik
- first_name: Daniel
  full_name: Virosztek, Daniel
  id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
  last_name: Virosztek
  orcid: 0000-0003-1109-5511
citation:
  ama: Pitrik J, Virosztek D. Quantum Hellinger distances revisited. <i>Letters in
    Mathematical Physics</i>. 2020;110(8):2039-2052. doi:<a href="https://doi.org/10.1007/s11005-020-01282-0">10.1007/s11005-020-01282-0</a>
  apa: Pitrik, J., &#38; Virosztek, D. (2020). Quantum Hellinger distances revisited.
    <i>Letters in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s11005-020-01282-0">https://doi.org/10.1007/s11005-020-01282-0</a>
  chicago: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.”
    <i>Letters in Mathematical Physics</i>. Springer Nature, 2020. <a href="https://doi.org/10.1007/s11005-020-01282-0">https://doi.org/10.1007/s11005-020-01282-0</a>.
  ieee: J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” <i>Letters
    in Mathematical Physics</i>, vol. 110, no. 8. Springer Nature, pp. 2039–2052,
    2020.
  ista: Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters
    in Mathematical Physics. 110(8), 2039–2052.
  mla: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.”
    <i>Letters in Mathematical Physics</i>, vol. 110, no. 8, Springer Nature, 2020,
    pp. 2039–52, doi:<a href="https://doi.org/10.1007/s11005-020-01282-0">10.1007/s11005-020-01282-0</a>.
  short: J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.
date_created: 2020-03-25T15:57:48Z
date_published: 2020-08-01T00:00:00Z
date_updated: 2023-08-18T10:17:26Z
day: '01'
department:
- _id: LaEr
doi: 10.1007/s11005-020-01282-0
ec_funded: 1
external_id:
  arxiv:
  - '1903.10455'
  isi:
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intvolume: '       110'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
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  url: https://arxiv.org/abs/1903.10455
month: '08'
oa: 1
oa_version: Preprint
page: 2039-2052
project:
- _id: 26A455A6-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '846294'
  name: Geometric study of Wasserstein spaces and free probability
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Quantum Hellinger distances revisited
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 110
year: '2020'
...