caa a22 4500 445858680 CHVBK 20180317145436.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10946-011-9218-y doi (NATIONALLICENCE)springer-10.1007/s10946-011-9218-y A new form of symplectically invariant multimode uncertainty relations [Elektronische Daten] [Pavel Alekseev, Fedor Moroseev] We derive symplectically invariant uncertainty relations for a set of canonically conjugated variables. The uncertainty relations obtained are multimode analogs of the Robertson-Schrödinger inequalities. Our uncertainty relations are equivalent to the necessary and sufficient conditions for a matrix to be a correlation matrix of some quantum state, obtained by R. Simon and coauthors. The advantage of our inequalities, compared to that suggested by Simon, consists in its simplicity and more obvious symplectic invariance. We derive our inequalities for the case of a two-mode system in explicit form. Particular cases of small and large degrees of correlation between the first and second modes are analyzed in detail. Springer Science+Business Media, Inc., 2011 uncertainty relations nationallicence symplectic invariance nationallicence two-mode quantum state of light nationallicence Alekseev Pavel A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, Politekhnicheskaya Street 26, 194021, Saint Petersburg, Russia aut Moroseev Fedor A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, Politekhnicheskaya Street 26, 194021, Saint Petersburg, Russia aut Journal of Russian Laser Research Springer US; http://www.springer-ny.com 32/4(2011-07-01), 311-316 1071-2836 32:4<311 2011 32 10946 https://doi.org/10.1007/s10946-011-9218-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10946-011-9218-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alekseev Pavel A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, Politekhnicheskaya Street 26, 194021, Saint Petersburg, Russia aut NATIONALLICENCE 700 1- Moroseev Fedor A. F. Ioffe Physical-Technical Institute, Russian Academy of Sciences, Politekhnicheskaya Street 26, 194021, Saint Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Russian Laser Research Springer US; http://www.springer-ny.com 32/4(2011-07-01), 311-316 1071-2836 32:4<311 2011 32 10946 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer