  Precise determination of top-quark pairs is an essential tool for
understanding the overall consistency of the standard model (SM) expectations,
understanding limited New Physics (NP) models, through spin-spin correlation
and polarization parameters, and has a critical impact on the analyses
strategies at upcoming LHC programs. In this work, we review and discuss
various state-of-the-art Monte Carlo (MC) methodologies as
\textsc{MadGraph5}\_aMC@NLO, \textsc{Sherpa}, \textsc{Powheg-Box} and
\textsc{Pythia8}, which are Matrix Element (ME)$/$Parton Shower (PS) matching
generators including a complete set of spin correlation and polarization in top
quark pair production with dileptonic final states. This is the first such
study that not only compares the effects of different MC event generator
approaches on spin density matrix elements and polarization parameters, but
also investigates the effects of leading order (LO) and next-to-leading order
(NLO) accuracy in QCD, and electroweak (EW) corrections via \textsc{Sherpa}.
Moreover, as a continuation of the work, the prospects for possible NP
scenarios through top-quark spin-spin correlation and polarization measurements
for Supersymmetry (R parity conserved and violated models) and Dark Matter (top
quarks associated mediator) models during upcoming LHC runs are briefly
outlined. We find that all SM MC predictions for the defined set of variables
are generally consistent with the experimental data and theoretical predictions
within the uncertainty variations. Besides, for the distributions of the
$\cos\varphi$, laboratory-frame observables ($\cos\varphi_{lab}$ and
$|\Delta\phi_{ll}|$) and the observables generated by parity (P) and
charge-parity (CP) conserving interactions, we conclude some clues that the
considered signals and beyond may well be separated from experimental data and
located above the SM predictions.
