40 citations · 87 across the 12 of their papers we have counts for
12 papers
SIC dimension towers via cyclotomic polynomials
Gary McConnell
We prove a structure theorem for the dimension towers~ which arise in the number-theoretic formulation of Zauner's SIC-POVM conjecture over a real quadratic fi…
How Stark units enter SIC overlaps
Ingemar Bengtsson, Gary McConnell
It has been observed that the mutual scalar products of the vectors in a SIC-POVM are given by algebraic units, and at least in some cases by square roots of Stark units. The full…
Some new infinite families of non--rational real quadratic fields
Gary McConnell
Fix a finite collection of primes , not containing or . Using some observations which arose from attempts to solve the SIC-POVMs problem in quantum information, w…
SIC-POVMs from Stark Units: Dimensions n^2+3=4p, p prime
Ingemar Bengtsson, Markus Grassl, Gary McConnell
The existence problem for maximal sets of equiangular lines (or SICs) in complex Hilbert space of dimension remains largely open. In a previous publication (arXiv:2112.05552) w…
SIC-POVMs from Stark units: Prime dimensions n^2+3
Marcus Appleby, Ingemar Bengtsson, Markus Grassl +2
We propose a recipe for constructing a SIC fiducial vector in complex Hilbert space of dimension of the form , focussing on prime dimensions . Such structures are sho…
Evidence for and against Zauner's MUB Conjecture in
Gary McConnell, Harry Spencer, Afaq Tahir
The problem of finding provably maximal sets of mutually unbiased bases in , for composite dimensions which are not prime powers, remains completely open. In the…