The Heisenberg uncertainty principle is one of the cornerstones of quantum mechanics. We show that the observable values of the electromagnetic field in the far- and near-field zones emitted by the quantum nanoantenna are coupled via uncertainty relations of the Heisenberg type. The similar uncertainty inequalities are obtained for the electric currents in the different branches of the quantum networks. Based on these, we predict the mechanism of high-level squeezing of light in the quantum antennas. We show that this mechanism is highly directive. The strong values of squeezing are reaching in the narrow directions of high emission (tops of the main lobes of the radiation pattern). We also discuss the quantum noise manifestation in nanoelectronics and nanophotonics from the point of the electromagnetic compatibility of nanoelectronic devices, densely placed in the limited areas of space.