Quantum operation sharing with symmetric and asymmetric W states

Two tripartite schemes for sharing a single-qubit operation on a remote target state are proposed with symmetric and asymmetric W states, respectively. They are treated and compared from the aspects of quantum resource consumption, operation complexity, classical resource consumption, success probability and efficiency. It is found that the first scheme is better than the second one. In particular, the sharing can be achieved probabilistically with the first scheme while deterministically with the second one.