  Distinguishability is a fundamental and operational task generally connected
to information applications. In quantum information theory, from the postulates
of quantum mechanics it often has an intrinsic limitation, which then dictates
and also characterises capabilities of related information tasks. In this work,
we consider discrimination between bipartite two-qubit unitary transformations
by local operations and classical communication (LOCC) and its relations to
entangling capabilities of given unitaries. We show that a pair of entangling
unitaries which do not contain local parts, if they are perfectly
distinguishable by global operations, can also be perfectly distinguishable by
LOCC. There also exist non-entangling unitaries, e.g. local unitaries, that are
perfectly discriminated by global operations but not by LOCC. The results show
that capabilities of LOCC are strictly restricted than global operations in
distinguishing bipartite unitaries for a finite number of repetitions, contrast
to discrimination of a pair of bipartite states and also to asymptotic
discrimination of unitaries.
