Abstract: The correlation of a quantum system $A$ to an initially correlated system $E$ generally decreases when $A$ undergoes an evolution separated from $E$. Here we study the conditions under which the correlation disappears completely, resulting in a decoupling of $A$ from $E$. Decoupling is a general way to prove many coding theorems in quantum information theory. However existing decoupling constructions use random unitaries which are inefficient to implement. Hence the quest for derandomization.