  Starting from the Kauffman-Lomonaco braiding matrix transforming the natural
basis to Bell states, the spectral parameter describing the entanglement is
introduced through Yang-Baxterization. It gives rise to a new type of solutions
for Yang-Baxter equation, called the type-II that differs from the familiar
solution called type-I of YBE associated with the usual chain models. The
Majorana fermionic version of type-II yields the Kitaev Hamiltonian. The
introduced $\ell_1$ -norm leads to the maximum of the entanglement by taking
the extreme value and shows that it is related to the Wigner's D-function.
Based on the Yang-Baxter equation the 3-body S-Matrix for type-II is explicitly
given. Different from the type-I solution, the type-II solution of YBE should
be considered in describing quantum information. The idea is further extended
to $\mathbb{Z}_3$ parafermion model based on $SU(3)$ principal representation.
The type-II is in difference from the familiar type-I in many respects. For
example, the quantities corresponding to velocity in the chain models obey the
Lorentzian additivity $\frac{u+v}{1+uv}$ rather than Galilean rule $(u+v)$.
Most possibly, for the type-II solutions of YBE there may not exist RTT
relation. Further more, for $\mathbb{Z}_3$ parafermion model we only need the
rational Yang-Baxterization, which seems like trigonometric. Similar
discussions are also made in terms of generalized Yang-Baxter equation with
three spin spaces $\{1,\frac{1}{2},\frac{1}{2}\}$.
