  We revisit in detail the non-mean-field ground-state phase diagram for a
binary mixture of spin-1 Bose-Einstein condensates including quantum
fluctuations. The non-commuting terms in the spin-dependent Hamiltonian under
single spatial mode approximation make it difficult to obtain exact
eigenstates. Utilizing the spin z-component conservation and the total spin
angular momentum conservation, we numerically derive the information of the
building blocks and evaluate von Neumann entropy to quantify the ground states.
The mean-field phase boundaries are found to remain largely intact, yet the
ground states show fragmented and entangled behaviors within large parameter
spaces of interspecies spin-exchange and singlet-pairing interactions.
