Complex lines with restricted angles
Complex lines with restricted angles
Equiangular lines, mutually unbiased bases, and spin models
European Journal of Combinatorics
Quantum Information & Computation
Optimal fingerprinting strategies with one-sided error
Quantum Information & Computation
Computing Equiangular Lines in Complex Space
Mathematical Methods in Computer Science
Bounds for codes and designs in complex subspaces
Journal of Algebraic Combinatorics: An International Journal
The monomial representations of the Clifford group
Quantum Information & Computation
Galois automorphisms of a symmetric measurement
Quantum Information & Computation
Systems of imprimitivity for the clifford group
Quantum Information & Computation
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An element $\mathbf {z}\in \mathbb {CP}^{d-1}$ is called fiducial if {gz:g驴G} is a set of lines with only one angle between each pair, where G 驴驴 d 脳驴 d is the one-dimensional finite Weyl-Heisenberg group modulo its centre. We give a new characterization of fiducial vectors. Using this characterization, we show that the existence of almost flat fiducial vectors implies the existence of certain cyclic difference sets. We also prove that the construction of fiducial vectors in prime dimensions 7 and 19 due to Appleby (J. Math. Phys. 46(5):052107, 2005) does not generalize to other prime dimensions (except for possibly a set with density zero). Finally, we use our new characterization to construct fiducial vectors in dimension 7 and 19 whose coordinates are real.