  Single state saturation of the temporal correlation function is a key
condition to extract physical observables such as energies and matrix elements
of hadrons from lattice QCD simulations. A method commonly employed to check
the saturation is to seek for a plateau of the observables for large Euclidean
time. Identifying the plateau in the cases having nearby states, however, is
non-trivial and one may even be misled by a fake plateau. Such a situation
takes place typically for the system with two or more baryons. In this study,
we demonstrate explicitly the danger from a possible fake plateau in the
temporal correlation functions mainly for two baryons ($\Xi\Xi$ and $NN$), and
three and four baryons ($^3{\rm He}$ and $^4{\rm He})$ as well, employing
(2+1)-flavor lattice QCD at $m_{\pi}=0.51$ GeV on four lattice volumes with
$L=$ 2.9, 3.6, 4.3 and 5.8 fm. Caution is given for drawing conclusion on the
bound $NN$, $3N$ and $4N$ systems only based on the temporal correlation
functions.
