  We prove that there is a trade-off relation between the entanglement cost and
the number of rounds of communication, for two distant parties to accomplish a
bidirectional quantum information task by local operations and classical
communication (LOCC). We consider an implementation of a class of two-qubit
controlled-unitary gate by LOCC assisted by shared entanglement, in an
information theoretical scenario of asymptotically many input pairs and
vanishingly small error. We prove the trade-off relation by showing that one
ebit of entanglement per pair is necessary to be consumed for implementing the
unitary by any two-round protocol, whereas the entanglement cost by a
four-round protocol is strictly smaller than one ebit per pair.
