Correlations in open quantum systems and associated uncertainty relations - art. no. 062106

We study how correlations in a state of an open quantum system affect the i ntrinsic uncertainties of the expectation values of an arbitrary pair of no ncommuting observables. We show that for such observables, there exist Heis enberg-type uncertainty relations that take fully into account correlations in the state of the system. If the quantum system is in a pure state, such uncertainty relations reduce to the conventional one. We obtain an equatio n for the density operator of a general state that minimizes the new uncert ainty relations, and demonstrate that in the important case of coordinate a nd momentum operators, the minimum-uncertainty states are displaced squeeze d thermal states.