caa a22 4500 445858354 CHVBK 20180317145435.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10946-011-9189-z doi (NATIONALLICENCE)springer-10.1007/s10946-011-9189-z Unitary and non-unitary matrices as a source of different bases of operators acting on hilbert spaces [Elektronische Daten] [Sergey Filippov, Vladimir Man'ko] Columns of d 2 ×N matrices are shown to create different sets of N operators acting on d-dimensional Hilbert space. This construction corresponds to a formalism of the star-product of operator symbols. The known bases are shown to be partial cases of generic formulas derived using d 2 ×N matrices as a source for constructing arbitrary bases. The known examples of the SIC-POVM, MUBs, and the phase-space description of qubit states are considered from the viewpoint of the unified approach developed. Star-product schemes are classified with respect to associated d 2 ×N matrices. In particular, unitary matrices correspond to self-dual schemes. Such self-dual star-product schemes are shown to be determined by dequantizers which do not form the POVM. Springer Science+Business Media, Inc., 2011 finite-dimensional Hilbert space nationallicence basis of operators nationallicence star-product scheme nationallicence unitary matrix nationallicence self-dual scheme nationallicence Filippov Sergey Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, 141700, Moscow Region, Russia aut Man'ko Vladimir Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, 141700, Moscow Region, Russia aut Journal of Russian Laser Research Springer US; http://www.springer-ny.com 32/1(2011-01-01), 56-67 1071-2836 32:1<56 2011 32 10946 https://doi.org/10.1007/s10946-011-9189-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10946-011-9189-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Filippov Sergey Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, 141700, Moscow Region, Russia aut NATIONALLICENCE 700 1- Man'ko Vladimir Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, 141700, Moscow Region, Russia aut NATIONALLICENCE 773 0- Journal of Russian Laser Research Springer US; http://www.springer-ny.com 32/1(2011-01-01), 56-67 1071-2836 32:1<56 2011 32 10946 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer