Jones index, secret sharing and total quantum dimension

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dc.identifier.uri http://dx.doi.org/10.15488/1207
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/1231
dc.contributor.author Fiedler, Leander
dc.contributor.author Naaijkens, Pieter
dc.contributor.author Osborne, Tobias J.
dc.date.accessioned 2017-03-17T10:51:56Z
dc.date.available 2017-03-17T10:51:56Z
dc.date.issued 2017
dc.identifier.citation Fiedler, L.; Naaijkens, P.; Osborne, T.J.: Jones index, secret sharing and total quantum dimension. In: New Journal of Physics 19 (2017), Nr. 2, 23039. DOI: https://doi.org/10.1088/1367-2630/aa5c0c
dc.description.abstract We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible to a malicious party, and argue that the total quantum dimension quantifies how well we can perform this task. We then argue that this can be made mathematically rigorous using the index theory of subfactors, originally due to Jones and later extended by Kosaki and Longo. This theory provides us with a 'relative entropy' of two von Neumann algebras and a quantum channel, and we argue how these can be used to quantify how much classical information two parties can hide form an adversary. We also review the total quantum dimension in finite systems, in particular how it relates to topological entanglement entropy. It is known that the latter also has an interpretation in terms of secret sharing schemes, although this is shown by completely different methods from ours. Our work provides a different and independent take on this, which at the same time is completely mathematically rigorous. This complementary point of view might be beneficial, for example, when studying the stability of the total quantum dimension when the system is perturbed. eng
dc.description.sponsorship ERC/QFTCMPS
dc.description.sponsorship ERC/SIQS
dc.description.sponsorship DFG/EXC/201
dc.description.sponsorship EU/Horizon 2020
dc.description.sponsorship ERC/DQSIM
dc.language.iso eng
dc.publisher Bristol : Institute of Physics Publishing
dc.relation.ispartofseries New Journal of Physics 19 (2017), Nr. 2
dc.rights CC BY 3.0
dc.rights.uri https://creativecommons.org/licenses/by/3.0/
dc.subject quantum dimension eng
dc.subject quantum information eng
dc.subject secret sharing eng
dc.subject thermodynamic limit eng
dc.subject topological ordered states eng
dc.subject Entropy eng
dc.subject Information theory eng
dc.subject Quantum optics eng
dc.subject Quantum theory eng
dc.subject Topology eng
dc.subject Ordered state eng
dc.subject Thermodynamic limits eng
dc.subject Quantum entanglement eng
dc.subject.ddc 530 | Physik ger
dc.title Jones index, secret sharing and total quantum dimension
dc.type Text
dc.type article
dc.relation.issn 1367-2630
dc.relation.doi https://doi.org/10.1088/1367-2630/aa5c0c
dc.bibliographicCitation.issue 2
dc.bibliographicCitation.volume 19
dc.bibliographicCitation.firstPage 23039
tib.accessRights frei zug�nglich


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