The (Heisenberg) uncertainty is a specific, computable quantity associated with the expectation value of an operator for a given quantum state. If that state is

The (Heisenberg) uncertainty is a specific, computable quantity associated with the expectation value of an operator for a given quantum state. If that state is an eigenstate of the operator to be measured, the uncertainty is exactly zero. The only way for a state to have a non-zero uncertainty in its expectation value is if it is a superposition of more than one eigenstate with different eigenvalues. So I stand by my "superposition" phrasing. :) Taking a measurement of a system that is in a superposition of distinct eigenstates of the observable being measured will give a probabilistic distribution of measurement outcomes (with probabilities derived from the amplitudes of the corresponding terms in the superposition).