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Holonomy in Quantum Information Geometry
Stockholms universitet, Fysikum.ORCID iD: 0000-0002-1726-4892
2018 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we provide a uniform treatment of the two most popular non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sjöqvist et al. We develop a holonomy theory for the latter which we also relate to the already existing theory for the former. This makes it clear what the similarities and differences between the two geometric phases are. We discuss and motivate constraints on the two phases. Furthermore, we discuss some topological properties of the holonomy of `real' quantum systems, and we introduce higher-order geometric phases for not necessarily cyclic dynamical systems of mixed states. In a final chapter we apply the theory developed for the geometric phase of Sjöqvist et al. to geometric uncertainty relations, including some new "quantum speed limits''.

Place, publisher, year, edition, pages
Stockholm University , 2018.
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-90779OAI: oai:DiVA.org:kau-90779DiVA, id: diva2:1675493
Presentation
2018-03-21, C5:1007, Fysikum, Albanova universitetscentrum, 10:15 (English)
Opponent
Supervisors
Available from: 2022-06-23 Created: 2022-06-23 Last updated: 2022-06-23Bibliographically approved

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Andersson, Ole

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • apa.csl
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf