LEADER 02647nam 2200445 450 001 9910484121403321 005 20220127173054.0 010 $a3-030-76104-5 035 $a(CKB)4100000011950124 035 $a(MiAaPQ)EBC6634975 035 $a(Au-PeEL)EBL6634975 035 $a(OCoLC)1253477267 035 $a(PPN)255884370 035 $a(EXLCZ)994100000011950124 100 $a20220127d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA first course in the sporadic SICs /$fBlake C. Stacey 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$dİ2021 215 $a1 online resource (119 pages) 225 1 $aSpringerBriefs in mathematical physics ;$vVolume 41 311 $a3-030-76103-7 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- 1 Equiangular Lines -- 1.1 Introduction -- 1.2 Real Lines -- 1.3 Complex Lines -- References -- 2 Optimal Quantum Measurements -- 2.1 Introduction -- 2.2 SIC Representations of Quantum States -- 2.3 Constructing SICs Using Groups -- References -- 3 Geometry and Information Theory for Qubits and Qutrits -- 3.1 Qubits -- 3.2 Qutrits -- 3.3 Coherence -- References -- 4 SICs and Bell Inequalities -- 4.1 Mermin's Three-Qubit Bell Inequality -- 4.2 The Hoggar SIC -- 4.3 Qubit Pairs and Twinned Tetrahedral SICs -- 4.4 Failure of Hidden Variables for Qutrits -- 4.5 Quantum Theory from Nonclassical Probability Meshing -- References -- 5 The Hoggar-Type SICs -- 5.1 Introduction -- 5.2 Simplifying the QBic Equation -- 5.3 Triple Products and Combinatorial Designs -- 5.4 The Twin of the Hoggar SIC -- 5.5 Combinatorial Designs from the Twin Hoggar SIC -- 5.6 Quantum-State Compatibility -- 5.7 From Pauli Operators to Real Equiangular Lines -- 5.8 Concluding Remarks -- References -- 6 Sporadic SICs and the Exceptional Lie Algebras -- 6.1 Root Systems and Lie Algebras -- 6.2 E6 -- 6.3 E8 -- 6.4 E7 -- 6.5 The Regular Icosahedron and Real-Vector-Space Quantum Theory -- 6.6 Open Puzzles Concerning Exceptional Objects -- References -- 7 Exercises -- References -- Appendix Index -- Index. 410 0$aSpringerBriefs in mathematical physics ;$vVolume 41. 606 $aQuantum theory$xMathematics 615 0$aQuantum theory$xMathematics. 676 $a530.12 700 $aStacey$b Blake C.$0913356 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910484121403321 996 $aA First Course in the Sporadic SICs$92045961 997 $aUNINA