caa a22 4500 467906513 CHVBK 20180406152835.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10701-006-9060-1 doi (NATIONALLICENCE)springer-10.1007/s10701-006-9060-1 Gudder Stan Department of Mathematics, University of Denver, 80208, Denver, Colorado, USA aut Quantum Mechanics on Finite Groups [Elektronische Daten] [Stan Gudder] Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements in this framework. Springer Science+Business Media, Inc., 2006 quantum computation nationallicence finite groups nationallicence quantum operations nationallicence hidden subgroups nationallicence Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/8(2006-08-01), 1160-1192 0015-9018 36:8<1160 2006 36 10701 https://doi.org/10.1007/s10701-006-9060-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-006-9060-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gudder Stan Department of Mathematics, University of Denver, 80208, Denver, Colorado, USA aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/8(2006-08-01), 1160-1192 0015-9018 36:8<1160 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer