  Starting with the valence bond solid (VBS) ground state of the 1D AKLT
Hamiltonian, we make a partition of the system in 2 subsystems $A$ and $B$,
where $A$ is a block of $L$ consecutive spins and $B$ is it's complement. In
that setting we compute the partial transpose density matrix with respect to
$A$, $\rho^{T_A}$. We obtain the spectrum of the transposed density matrix of
the VBS pure system. Subsequently we define two disjoint blocks, $A$ and $B$
containing $L_A$ and $L_B$ spins respectively, separated by $L$ sites. Tracing
away the spins which do not belong to $A\cup B$, we find an expression for the
reduced density matrix of the $A$ and $B$ blocks $\rho(A,B)$. With this
expression (in the thermodynamic limit), we compute the entanglement spectrum
and other several entanglement measures, as the purity $P={\rm
tr}(\rho(A,B)^2)$, the negativity $\mathcal{N}$, and the mutual entropy.
