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Open AccessArticle

The Poincaré Half-Plane for Informationally-Complete POVMs

Institut FEMTO-ST CNRS UMR 6174, Université de Bourgogne/Franche-Comté, 15 B Avenue des Montboucons, F-25044 Besançon, France
Entropy 2018, 20(1), 16; https://doi.org/10.3390/e20010016
Received: 12 October 2017 / Revised: 22 November 2017 / Accepted: 28 December 2017 / Published: 31 December 2017
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
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. View Full-Text
Keywords: informationally-complete POVMs; modular group; quantum computing informationally-complete POVMs; modular group; quantum computing
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Planat, M. The Poincaré Half-Plane for Informationally-Complete POVMs. Entropy 2018, 20, 16.

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