View in EDS

Functional calculus of quantum channels for the holomorphic discrete series of SU(1,1)

Saved in:
Bibliographic Details
Title: Functional calculus of quantum channels for the holomorphic discrete series of SU(1,1)
Authors: van Haastrecht, Robin, 2000
Source: Journal of Functional Analysis. 289(6)
Subject Terms: Wehrl inequality, Quantum channels, Reproducing kernels, Hermitian symmetric spaces
Description: The tensor product of two holomorphic discrete series representations of SU(1,1) can be decomposed as a direct multiplicity-free sum of infinitely many holomorphic discrete series representations. I shall introduce equivariant quantum channels for each component of the direct sum by mapping the tensor product of an operator and the identity onto the projection onto one of the irreducible components, generalizing the construction of pure equivariant quantum channels for compact groups. Then I calculate the functional calculus of this operator for polynomials and prove a limit formula for the trace of the functional calculus for any differentiable function. The methods I used are the theory of reproducing kernel Hilbert spaces and a Plancherel theorem for the disk D=SU(1,1)/U(1), together with exact constants for the eigenvalues of the Berezin transform. I prove that the limit of the trace of the functional calculus can be expressed using generalized Husimi functions or using Berezin transforms.
File Description: electronic
Access URL: https://research.chalmers.se/publication/546322
https://research.chalmers.se/publication/546322/file/546322_Fulltext.pdf
Database: SwePub
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://research.chalmers.se/publication/546322#
    Name: EDS - SwePub (s4221598)
    Category: fullText
    Text: View record in SwePub
  – Url: https://resolver.ebscohost.com/openurl?sid=EBSCO:edsswe&genre=article&issn=00221236&ISBN=&volume=289&issue=6&date=20250101&spage=&pages=&title=Journal of Functional Analysis&atitle=Functional%20calculus%20of%20quantum%20channels%20for%20the%20holomorphic%20discrete%20series%20of%20SU%281%2C1%29&aulast=van%20Haastrecht%2C%20Robin&id=DOI:10.1016/j.jfa.2025.111036
    Name: Full Text Finder
    Category: fullText
    Text: Full Text Finder
    Icon: https://imageserver.ebscohost.com/branding/images/FTF.gif
    MouseOverText: Full Text Finder
  – Url: https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=EBSCO&SrcAuth=EBSCO&DestApp=WOS&ServiceName=TransferToWoS&DestLinkType=GeneralSearchSummary&Func=Links&author=van%20Haastrecht%20R
    Name: ISI
    Category: fullText
    Text: Nájsť tento článok vo Web of Science
    Icon: https://imagesrvr.epnet.com/ls/20docs.gif
    MouseOverText: Nájsť tento článok vo Web of Science
Header DbId: edsswe
DbLabel: SwePub
An: edsswe.oai.research.chalmers.se.4c03ae14.5f7c.4863.9a99.1c01d316bb64
RelevancyScore: 1065
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 1064.736328125
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Functional calculus of quantum channels for the holomorphic discrete series of SU(1,1)
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22van+Haastrecht%2C+Robin%22">van Haastrecht, Robin</searchLink>, 2000
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <i>Journal of Functional Analysis</i>. 289(6)
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Wehrl+inequality%22">Wehrl inequality</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+channels%22">Quantum channels</searchLink><br /><searchLink fieldCode="DE" term="%22Reproducing+kernels%22">Reproducing kernels</searchLink><br /><searchLink fieldCode="DE" term="%22Hermitian+symmetric+spaces%22">Hermitian symmetric spaces</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: The tensor product of two holomorphic discrete series representations of SU(1,1) can be decomposed as a direct multiplicity-free sum of infinitely many holomorphic discrete series representations. I shall introduce equivariant quantum channels for each component of the direct sum by mapping the tensor product of an operator and the identity onto the projection onto one of the irreducible components, generalizing the construction of pure equivariant quantum channels for compact groups. Then I calculate the functional calculus of this operator for polynomials and prove a limit formula for the trace of the functional calculus for any differentiable function. The methods I used are the theory of reproducing kernel Hilbert spaces and a Plancherel theorem for the disk D=SU(1,1)/U(1), together with exact constants for the eigenvalues of the Berezin transform. I prove that the limit of the trace of the functional calculus can be expressed using generalized Husimi functions or using Berezin transforms.
– Name: Format
  Label: File Description
  Group: SrcInfo
  Data: electronic
– Name: URL
  Label: Access URL
  Group: URL
  Data: <link linkTarget="URL" linkTerm="https://research.chalmers.se/publication/546322" linkWindow="_blank">https://research.chalmers.se/publication/546322</link><br /><link linkTarget="URL" linkTerm="https://research.chalmers.se/publication/546322/file/546322_Fulltext.pdf" linkWindow="_blank">https://research.chalmers.se/publication/546322/file/546322_Fulltext.pdf</link>
PLink https://erproxy.cvtisr.sk/sfx/access?url=https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsswe&AN=edsswe.oai.research.chalmers.se.4c03ae14.5f7c.4863.9a99.1c01d316bb64
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jfa.2025.111036
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Wehrl inequality
        Type: general
      – SubjectFull: Quantum channels
        Type: general
      – SubjectFull: Reproducing kernels
        Type: general
      – SubjectFull: Hermitian symmetric spaces
        Type: general
    Titles:
      – TitleFull: Functional calculus of quantum channels for the holomorphic discrete series of SU(1,1)
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: van Haastrecht, Robin
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 00221236
            – Type: issn-print
              Value: 10960783
            – Type: issn-locals
              Value: SWEPUB_FREE
            – Type: issn-locals
              Value: CTH_SWEPUB
          Numbering:
            – Type: volume
              Value: 289
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: Journal of Functional Analysis
              Type: main
ResultId 1