On Weyl-Heisenberg orbits of equiangular lines

A Necessary Condition for Weyl-Heisenberg Frames

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Some remarks on Heisenberg frames and sets of equiangular lines

We consider the long standing problem of constructing d equiangular lines in C, i.e., finding a set of d unit vectors (φj) in C d with |〈φj , φk〉| = 1 √ d + 1 , j 6= k. Such ‘equally spaced configurations’ have appeared in various guises, e.g., as complex spherical 2–designs, equiangular tight frames, isometric embeddings `2(d) → `4(d), and most recently as SICPOVMs in quantum measurement theor...

Generating Ray Class Fields of Real Quadratic Fields via Complex Equiangular Lines

Let K be a real quadratic field. For certain K with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of K using a numerical method that arose in the study of complete sets of equiangular lines in C (known in quantum information as symmetric informationally complete measurements or sics). The construction in low dimensions suggests a general recip...

p-MECHANICS AND DE DONDER–WEYL THEORY

The orbit method of Kirillov is used to derive the p-mechanical brackets [25]. They generate the quantum (Moyal) and classic (Poisson) brackets on respective orbits corresponding to representations of the Heisenberg group. The extension of p-mechanics to field theory is made through the De Donder–Weyl Hamiltonian formulation. The principal step is the substitution of the Heisenberg group with G...