  We present the generalized version of Wang's protocol[A.M.Wang, Phys.Rev.A
74,032317 (2006)] for the remote implementation(sometimes referred to as
quantum remote control) of partially unknown quantum operations. The protocol
only requires no more than half of the entanglements used in Bidirectional
Quantum State Teleportation. We also propose a protocol for another form of
quantum remote control. It can remotely implement a unitary operation which is
a combination of the projective representations of a group. Moreover, we prove
that the Schmidt rank of the entanglements cannot not be less than the number
of controlled parameters of the operations, which for the first time gives a
lower bound on entanglement costs in remote implementation of quantum
operations.
