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  • 1
    Online-Ressource
    Online-Ressource
    Cham :Springer International Publishing :
    UID:
    almahu_9949070879202882
    Umfang: VIII, 115 p. 7 illus., 2 illus. in color. , online resource.
    Ausgabe: 1st ed. 2021.
    ISBN: 9783030761042
    Serie: SpringerBriefs in Mathematical Physics, 41
    Inhalt: This book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty. While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.
    Anmerkung: Equiangular Lines -- Sporadic SICs and the Exceptional Lie Algebras -- The Hoggar-type SICs.-SICs as Equicoherent Quantum States -- SICs and Bell Inequalities.
    In: Springer Nature eBook
    Weitere Ausg.: Printed edition: ISBN 9783030761035
    Weitere Ausg.: Printed edition: ISBN 9783030761059
    Sprache: Englisch
    URL: Volltext  (URL des Erstveröffentlichers)
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Online-Ressource
    Online-Ressource
    Cham : Springer
    UID:
    gbv_1759343072
    Umfang: 1 Online-Ressource (VIII, 115 Seiten)
    ISBN: 9783030761042
    Serie: SpringerBriefs in mathematical physics volume 41
    Inhalt: This book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty. While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level.
    Anmerkung: Equiangular Lines -- Sporadic SICs and the Exceptional Lie Algebras -- The Hoggar-type SICs.-SICs as Equicoherent Quantum States -- SICs and Bell Inequalities.
    Weitere Ausg.: ISBN 9783030761035
    Weitere Ausg.: ISBN 9783030761059
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Online-Ressource
    Online-Ressource
    Cham, Switzerland :Springer,
    UID:
    edoccha_9959854699402883
    Umfang: 1 online resource (119 pages)
    ISBN: 3-030-76104-5
    Serie: SpringerBriefs in mathematical physics ; Volume 41
    Anmerkung: Intro -- Preface -- Contents -- 1 Equiangular Lines -- 1.1 Introduction -- 1.2 Real Lines -- 1.3 Complex Lines -- References -- 2 Optimal Quantum Measurements -- 2.1 Introduction -- 2.2 SIC Representations of Quantum States -- 2.3 Constructing SICs Using Groups -- References -- 3 Geometry and Information Theory for Qubits and Qutrits -- 3.1 Qubits -- 3.2 Qutrits -- 3.3 Coherence -- References -- 4 SICs and Bell Inequalities -- 4.1 Mermin's Three-Qubit Bell Inequality -- 4.2 The Hoggar SIC -- 4.3 Qubit Pairs and Twinned Tetrahedral SICs -- 4.4 Failure of Hidden Variables for Qutrits -- 4.5 Quantum Theory from Nonclassical Probability Meshing -- References -- 5 The Hoggar-Type SICs -- 5.1 Introduction -- 5.2 Simplifying the QBic Equation -- 5.3 Triple Products and Combinatorial Designs -- 5.4 The Twin of the Hoggar SIC -- 5.5 Combinatorial Designs from the Twin Hoggar SIC -- 5.6 Quantum-State Compatibility -- 5.7 From Pauli Operators to Real Equiangular Lines -- 5.8 Concluding Remarks -- References -- 6 Sporadic SICs and the Exceptional Lie Algebras -- 6.1 Root Systems and Lie Algebras -- 6.2 E6 -- 6.3 E8 -- 6.4 E7 -- 6.5 The Regular Icosahedron and Real-Vector-Space Quantum Theory -- 6.6 Open Puzzles Concerning Exceptional Objects -- References -- 7 Exercises -- References -- Appendix Index -- Index.
    Weitere Ausg.: ISBN 3-030-76103-7
    Sprache: Englisch
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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