  We present an equivalence theorem to unify the two classes of uncertainty
relations, i.e., the variance-based ones and the entropic forms, which shows
that the entropy of an operator in a quantum system can be built from the
variances of a set of commutative operators. That means an uncertainty relation
in the language of entropy may be mapped onto a variance-based one, and vice
versa. Employing the equivalence theorem, alternative formulations of entropic
uncertainty relations stronger than existing ones in the literature are
obtained for qubit system, and variance based uncertainty relations for spin
systems are reached from the corresponding entropic uncertainty relations.
