  Coupled oscillators are among the simplest composite quantum systems in which
the interplay of entanglement and interaction may be explored. We examine the
effects of coupling on fluctuations of the coordinates and momenta of the
oscillators in a single-excitation entangled state. We discover that coupling
acts as a mechanism for noise transfer between one pair of coordinate and
momentum and another. Through this noise transfer mechanism, the uncertainty
product is lowered, on average, relatively to its non-coupled level for one
pair of coordinate and momentum and it is enhanced for the other pair. This
novel mechanism may be explored in precision measurements in
entanglement-assisted sensing and metrology.
