  We replace a Hamiltonian with a modular Hamiltonian in the spectral form
factor and the level spacing distribution function. This study establishes a
connection between quantities within Quantum Entanglement and Quantum Chaos. To
have a universal study for Quantum Entanglement, we consider the Gaussian
random 2-qubit model. The maximum violation of Bell's inequality demonstrates a
positive correlation with the entanglement entropy. Thus, the violation plays
an equivalent role as Quantum Entanglement. We first provide an analytical
estimation of the relation between quantum entanglement quantities and the dip
when a subregion only has one qubit. The time of the first dip is monotone for
entanglement entropy. The dynamics in a subregion is independent of the initial
state at a late time. It is one of the signaling conditions for classical
chaos. We also extend our analysis to the Gaussian random 3-qubit state, and it
indicates a similar result. The simulation shows that the level spacing
distribution function approaches GUE at a late time. In the end, we develop a
technique within QFT to the spectral form factor for its relation to an
$n$-sheet manifold. We apply the technology to a single interval in CFT$_2$ and
the spherical entangling surface in $\mathcal{N}=4$ super Yang-Mills theory.
The result is one for both cases, but the R\'enyi entropy can depend on the
R\'enyi index. For the case of CFT$_2$, it indicates the difference between the
continuum and discrete spectrum.
