Volume 11 Issue 2
The Poincaré Half-Plane for Informationally-Complete POVMs
Michel Planat
Institut FEMTO-ST CNRS UMR 6174, Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
Abstract
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 the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from the Poincaré upper half-plane model ℍ
. To do this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates, some of the eigenstates of which are the sought fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen–Specker theorem.
Keywords:
informationally-complete POVMs; modular group; quantum computingPACS:
03.67.-a; 03.65.Wj; 02.20.-a; 03.65.Fd; 03.65.Aa; 02.10.Ox; 03.65.Ud; 03.67.LxMSC:
11F06; 20H05; 81P50; 81P68; 81P13; 81P45; 20B05