Author(s): Blake C. Stacey
Series: Springer Briefs in Mathematical Physics vol. 41
Publisher: Springer
Year: 2021
Language: English
Pages: 119
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
