On Weyl-Heisenberg orbits of equiangular lines

On Weyl-Heisenberg orbits of equiangular lines

An element z ∈CPd−1 is called fiducial if {gz : g ∈G} is a set of lines with only one angle between each pair, where G∼= Zd × Zd 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. ...

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...

A Necessary Condition for Weyl-Heisenberg Frames

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

On the Heisenberg-weyl Inequality

In 1927, W. Heisenberg demonstrated the impossibility of specifying simultaneously the position and the momentum of an electron within an atom.The well-known second moment Heisenberg-Weyl inequality states: Assume that f : R → C is a complex valued function of a random real variable x such that f ∈ L(R). Then the product of the second moment of the random real x for |f | and the second moment o...