  We define a product between quantum superoperators which is preserved under
the Choi-Jamio{\l}kowski-Kraus-Sudarshan channel-state isomorphism. We then
identify the product as the convolution on the space of superoperators, with
respect to which the channel-state duality is also an algebra isomorphism. We
find that any witness operator for detecting nonseparability of quantum
operations on separated parties can be written entirely within the space of
superoperators with the help of the convolution product.
