Recent years have seen significant advances in the study of symmetric informationally
complete (SIC) quantum measurements, also known as maximal sets of complex …

A Grassmannian frame is a collection of unit vectors which are optimally incoherent. To date,
the vast majority of explicit Grassmannian frames are equiangular tight frames (ETFs). This …

Abstract For t∈{1, 2,…} fixed, a natural class of spherical designs is given by the vectors v
1,…, vn in F d= R d, C d (not all zero) which give equality in the bound∑ j= 1 n∑ k= 1 n|< vj …

We consider the general question of when all orbits under the unitary action of a finite group
give a complex spherical design. Those orbits which have large stabilisers are then good …

It has been shown in previous papers that classes of (minimal asymmetric) informationally-
complete positive operator valued measures (IC-POVMs) in dimension d can be built using …

We define the projective symmetry group of a finite sequence of vectors (a frame) in a
natural way as a group of permutations on the vectors (or their indices). This definition …

Many tight frames of interest are constructed via their Gramian matrix (which determines the
frame up to unitary equivalence). Given such a Gramian, it can be determined whether or not …

We show how the variational characterisation of spherical designs can be used to take a
union of spherical designs to obtain a spherical design of higher order (degree, precision …

We give a holomorphic quartic polynomial in the overlap variables whose zeros on the torus
are precisely the Weyl-Heisenberg SICs (symmetric informationally complete positive …