Construction, classification and parametrization of complex Hadamard matrices

Abstract

The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three chapters, each describing one of three distinct faces of this field whose treatment require various mathematical tools ranging from combinatorics, functional analysis to symbolic computation. Although we firmly believe that these beautiful objects are interesting on their own and worth investigating from a purely mathematical perspective we make considerable efforts to highlight some of their applications we aware of.

PhD thesis, 159 pages

References in corpus (1)

• Concrete Constructions of Real Equiangular Line Sets

Cited by in corpus (15)

• Equiangular lines in Euclidean spaces
• Biunitary constructions in quantum information
• Geometry of the set of mixed quantum states: An apophatic approach
• Isolated Hadamard Matrices from Mutually Unbiased Product Bases
• $BCCB$ complex Hadamard matrices of order 9, and MUBs
• Computing Puiseux Series for Algebraic Surfaces
• Perfect tight quantum teleportation without a shared reference frame
• Families of complex Hadamard matrices
• Invariants for maximally entangled vectors and unitary bases
• Temperley-Lieb R-matrices from generalized Hadamard matrices
• Block-Circulant Complex Hadamard Matrices
• Optimal quantum tomography with constrained elementary measurements arising from unitary bases
• Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing Unit
• Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem
• Robust Hadamard matrices, unistochastic rays in Birkhoff polytope and equi-entangled bases in composite spaces