The Poincaré half-plane for informationally complete POVMs

Abstract

It has been shown that classes of (minimal asymmetric) informationally complete POVMs in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states [M. Planat and Z. Gedik, R. Soc. open sci. 4, 170387 (2017)]. The latter states may also be derived starting from the Poincaré upper half-plane model H. For doing this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates whose some of the eigenstates are the seeked fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen-Specker theorem.

15 pages, 6 figs

References in corpus (2)

• On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits
• Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets

Cited by in corpus (1)

• Informationally complete characters for quark and lepton mixings