  Interaction-free measurement (IFM), just as its name implies, can enable one
to detect an object without interacting with it, i.e., substantially reducing
the damage to the object. With the help of quantum channel theory, we
investigate the general model of "quantum-Zeno-like" IFM, whose optics setup is
a Mach-Zehnder like interferometer utilizing the quantum Zeno effect, where the
object to be detected is semitransparent and the interrogation cycle number $N$
is finite. And we define two important probabilities $P_{\rm loss}$ and $P_{\rm
error}$ to evaluate the IFM process, which describe the photon loss rate and
the error of discriminating the presenece/absence of the object respectively.
The minimum values of these two probabilities and the corresponding initial
input states to reach them are attained via this model. And we find that when
the interrogation cycle $N$ approaches infinity, the object can be perfectly
detected, where the minimum values of these two probabilities are both zero and
the initial input state to reach them becomes the same state $|1\rangle$ in our
system. In addition, we also study whether quantum correlation can benefit IFM
or not, but the answer is no, in the sense that the entangled photon input
state cannot minimize $P_{\rm loss}$, $P_{\rm error}$ more than single photon
input state. Our work provides principal theoretic support for the practical
realization of IFM and the employed analysis technique can be applied to other
quantum facilitating scenarios.
