  We give a conceptually simple necessary condition such that a separable
quantum operation can be implemented by local operations on subsystems and
classical communication between parties (LOCC), a condition which follows from
a novel approach to understanding LOCC. This necessary condition holds for any
number of parties and any finite number of rounds of communication and as such,
also provides a completely general sufficient condition that a given separable
operation cannot be exactly implemented by LOCC. Furthermore, it demonstrates
an extremely strong difference between separable operations and LOCC, in that
there exist examples of the former for which the condition is extensively
violated. More precisely, the violation by separable operations of our
necessary condition for LOCC grows without limit as the number of parties
increases.
