  Recently, the problem of discriminating multipartite unitary operations by
local operations and classical communication (LOCC) has attracted significant
attention. The latest work in the literature on this problem showed that two
multipartite unitary operations can always be perfectly distinguished by LOCC
when a finite number of runs are allowable. However, in these schemes, local
entanglement (an entangled state holden by one party) was required, which seems
to imply that local entanglement is necessary for perfect discrimination
between unitary operations by LOCC. In this article, we show that a perfect
discrimination between two unitary operations acting on a two-qudits can always
be achieved without exploiting any entanglement. As a result, we conclude that
local entanglement is not necessary for perfect discrimination between unitary
operations acting on two-qudits by LOCC.
