What is an example of a measurement that is LOCC but not separable?

Could you give me an example of a measurement which is separable but not LOCC (Local Operations Classical Communication)?
Given an ensable of states $rho^{N}$, a separable measurement on it is a POVM $lbrace N_i rbrace$ where the effects $N_i$ are all of the form $N_i = A_i^{1} otimes A_i^{2} otimes dots otimes A_i^{N}$. So they are a separable product of effects acting on each state $rho$ in $rho^{N}$.

Note: Cross-posted on Physics SE.