Heisenberg Uncertainty Principle states (in the form of the Robertson-Schroedinger Formula) that measurement of two non-commuting observables has a limiting precision, even for flawless measurement devices. Okay, no problem with this. But what about a measurement on a single observable, does Quantum Mechanics imposes some fundamental limit?
p.s.: Googling around I found this paper which states "that an intrinsic quantum uncertainty on a single observable is ineludible in a number of physical situations", talking mainly about bipartite systems.