02647nam 2200445 450 991048412140332120220127173054.03-030-76104-5(CKB)4100000011950124(MiAaPQ)EBC6634975(Au-PeEL)EBL6634975(OCoLC)1253477267(PPN)255884370(EXLCZ)99410000001195012420220127d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA first course in the sporadic SICs /Blake C. StaceyCham, Switzerland :Springer,[2021]©20211 online resource (119 pages)SpringerBriefs in mathematical physics ;Volume 413-030-76103-7 Includes bibliographical references and index.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.SpringerBriefs in mathematical physics ;Volume 41.Quantum theoryMathematicsQuantum theoryMathematics.530.12Stacey Blake C.913356MiAaPQMiAaPQMiAaPQBOOK9910484121403321A First Course in the Sporadic SICs2045961UNINA