  In the present work, we consider a scenario where an arbitrary two-qubit pure
state is applied to generate a randomly distributed key via the generalized EPR
protocol. Using the twirling procedure to convert the pure state into a Werner
state, the error rate of the key can be reduced by a factor of $2/3$. This
effect indicates that entanglement is not the sufficient resource of the
generalized EPR protocol since it is not increased in the twirling procedure.
Instead of entanglement, the geometric discord is suggested to be the general
quantum resource for this task.
