Abstract
SIC-POVMs are configurations of points or rank-one projections arising from the action of a finite Heisenberg group on Cd. The resulting equations are interpreted in terms of moment maps by focussing attention on the orbit of a cyclic subgroup and the maximal torus in U(d) that contains it. The image of a SIC-POVM under the associated moment map lies in an intersection of real quadrics, which we describe explicitly. We also elaborate the conjectural description of the related number fields and describe the structure of Galois orbits of overlap phases.
Original language | English |
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Pages (from-to) | 502-531 |
Number of pages | 30 |
Journal | SIAM Journal on Applied Algebra and Geometry |
Volume | 4 |
Issue number | 4 |
DOIs | |
Publication status | Published - 10 Dec 2020 |