Interpolatability distinguishes LOCC from separable von Neumann measurements

Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations.