  Collective operations on a network of spatially-separated quantum systems can
be carried out using local quantum (LQ) operations, classical communication
(CC) and shared entanglement (SE). Such operations can also be used to
communicate classical information and establish entanglement between distant
parties. We show how these facts lead to measures of the inseparability of
quantum operations, and argue that a maximally-inseparable operation on 2
qubits is the SWAP operation. The generalisation of our argument to N qubit
operations leads to the conclusion that permutation operations are
maximally-inseparable. For even N, we find the minimum SE and CC resources
which are sufficient to perform an arbitrary collective operation. These
minimum resources are 2(N-1) ebits and 4(N-1) bits, and these limits can be
attained using a simple teleportation-based protocol. We also obtain lower
bounds on the minimum resources for the odd case. For all $N{\geq}4$, we show
that the SE/CC resources required to perform an arbitrary operation are
strictly greater than those that any operation can establish/communicate.
