  Controlled quantum teleportation (CQT) can be considered as a variant of
quantum teleportation in which three parties are involved where one party acts
as the controller. The usability of the CQT scheme depends on two types of
fidelities viz. conditioned fidelity and non-conditioned fidelity. The
difference between these fidelities may be termed as power of the controller
and it plays a vital role in the CQT scheme. Thus, our aim is to estimate the
power of the controller in such a way so that its estimated value can be
obtained in an experiment. To achieve our goal, we have constructed a witness
operator and have shown that its expected value may be used in the estimation
of the lower bound of the power of the controller. Furthermore, we have shown
that it is possible to make the standard W state useful in the CQT scheme if
one of its qubits either passes through the amplitude damping channel or the
phase damping channel. We have also shown that the phase damping channel
performs better than the amplitude damping channel in the sense of generating
more power of the controller in the CQT scheme.

Quantum Physics