Krusekamp, Sebastian: Nice Complete Sets of Pairwise Quasi-Orthogonal Masas : From the Basics to a Unique Encoding. 2014
Inhalt
- Introduction
- Motivation and subject classification
- Content and organisation of the present thesis
- Notations and conventions
- Maximal abelian *-subalgebras (masas) in the complex d-4mu-4mu d+1mu-matrices
- Motivation: Finite dimensional quantum systems and maximal abelian *-subalgebras
- Masas in the complex d-4mu-4mu d+1mu-matrices, and associated orthonormal bases and unitaries
- Complex Hadamard matrices
- Unitary Hilbert-Schmidt orthonormal bases of masas
- Quasi-orthogonality of masas
- Motivation: Pairs of mutually unbiased bases in quantum physics
- Quasi-orthogonal masas, unbiased bases and unbiased unitaries
- Measures of quasi-orthogonality
- Equivalent, standard, and non-standard pairs of quasi-orthogonal masas
- Excursion: Standard pairs of masas and crossed products
- Families of pairwise quasi-orthogonal masas
- Motivation: Optimal state-determination of quantum systems
- Maximal and complete families of pairwise quasi-orthogonal masas and the MUB-Problem
- Constructions of complete quasi-orthogonal families of masas in prime power dimensions
- A construction of quasi-orthogonal masa families in square dimensions
- Excursion: Mutually unbiased bases and design theory
- Nice masa families and the generalised Clifford algebra
- Nice unitary error bases
- Normal pairs of quasi-orthogonal masas
- Nice families of pairwise quasi-orthogonal masas
- Nice complete masa families in the generalised Clifford algebra
- Excursion: Concatenated normal pairs of masas
- Smid families
- Equivalence classes of smid families and nice sets of masas
- Complete linear smid families in the matrix algebras Metafont2p
- Smid families in Metafont2p, permutation polynomials, and Latin squares
- Smid families in small dimensions—some computer algebraic results
- Conclusion
- Appendix
- Bibliography
- List of figures
- List of symbols
- Index