  Neutrino and anti-neutrino states coming from the neutral current or $Z_0$
decay are blind with respect to the flavor. The neutrino oscillation is
observed and formulated when its flavor is known. However, it has been shown
that we can see neutrino oscillation pattern for $Z_0$ decay neutrinos provided
that both neutrino and anti-neutrino are detected. In this paper, we restudy
this oscillation via quantum field theory approach. Through this approach, we
find that the oscillation pattern ceases if the distance between the detectors
is larger than the coherence length, while both neutrino and antineutrino
states may be coherent. Also the uncertainty of source (region of $Z_0$ decay)
does not have any role in the coherency of neutrino and antineutrino.
