  Quantum entanglement under an extensive bipartition can reveal the critical
boundary theory of a topological phase in the parameter space. In this study we
demonstrate that the infinite-randomness fixed point for spin-1/2 degrees of
freedom can emerge from an extensive random bipartition of the spin-1
Affleck-Kennedy-Lieb-Tasaki chain. The nested entanglement entropy of the
ground state of the reduced density matrix exhibits a logarithmic scaling with
an effective central charge $\tilde{c} = 0.72 \pm 0.02 \approx \ln 2$. We
further discuss, in the language of bulk quantum entanglement, how to
understand all phase boundaries and the surrounding Griffiths phases for the
antiferromagnetic Heisenberg spin-1 chain with quenched disorder and
dimerization.
