caa a22 4500 467905967 CHVBK 20180406152834.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10701-005-9008-x doi (NATIONALLICENCE)springer-10.1007/s10701-005-9008-x Wootters W. Department of Physics, Williams College, 01267, Williamstown, MA, USA aut Quantum Measurements and Finite Geometry [Elektronische Daten] [W. Wootters] A complete set of mutually unbiased bases for a Hilbert space of dimension N is analogous in some respects to a certain finite geometric structure, namely, an affine plane. Another kind of quantum measurement, known as a symmetric informationally complete positive-operator-valued measure, is, remarkably, also analogous to an affine plane, but with the roles of points and lines interchanged. In this paper I present these analogies and ask whether they shed any light on the existence or non-existence of such symmetric quantum measurements for a general quantum system with a finite-dimensional state space. Springer Science+Business Media, Inc., 2006 affine plane nationallicence POVM nationallicence mutually unbiased bases nationallicence 03.65.Ta nationallicence 03.65.Wj nationallicence 02.10.Ox nationallicence Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/1(2006-01-01), 112-126 0015-9018 36:1<112 2006 36 10701 https://doi.org/10.1007/s10701-005-9008-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-005-9008-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wootters W. Department of Physics, Williams College, 01267, Williamstown, MA, USA aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/1(2006-01-01), 112-126 0015-9018 36:1<112 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer