  The problem behind this paper is, if the number of queries to unitary
operations is fixed, say $k$, then when do local operations and classical
communication (LOCC) suffice for optimally distinguishing bipartite unitary
operations? We consider the above problem for two-qubit unitary operations in
the case of $k=1$, showing that for two two-qubit entangling unitary operations
without local parties, LOCC achieves the same distinguishability as the global
operations. Specifically, we obtain: (i) if such two unitary operations are
perfectly distinguishable by global operations, then they are perfectly
distinguishable by LOCC too, and (ii) if they are not perfectly distinguishable
by global operations, then LOCC can achieve the same optimal discrimination
probability as the global operations.
