  Lattice thermal conductivity ($\kappa_{lat}$) of MgSiO$_3$ postperovskite
(MgPPv) under the Earth's lower mantle high pressure-temperature conditions is
studied using the phonon quasiparticle approach by combing \textit{ab initio}
molecular dynamics and lattice dynamics simulations. Phonon lifetimes are
extracted from the phonon quasiparticle calculations, and the phonon group
velocities are computed from the anharmonic phonon dispersions, which in
principle capture full anharmonicity. It is found that throughout the lowermost
mantle, including the D" region, $\kappa_{lat}$ of MgPPv is ~25% larger than
that of MgSiO$_3$ perovskite (MgPv), mainly due to MgPPv's higher phonon
velocities. Such a difference in phonon velocities between the two phases
originates in the MgPPv's relatively smaller primitive cell. Systematic results
of temperature and pressure dependences of both MgPPv's and MgPv's
$\kappa_{lat}$ are demonstrated.
