  For a generic $n$-qubit system, local invariants under the action of
$SL(2,\mathbb{C})^{\otimes n}$ characterize non-local properties of
entanglement. In general, such properties are not immediately apparent and hard
to construct. Here we consider certain two-qubit Yang-Baxter operators, which
we dub of the `X-type', and show that their eigenvalues completely determine
the non-local properties of the system. Moreover, we apply the Turaev procedure
to these operators and obtain their associated link/knot polynomials. We also
compute their entangling power and compare it with that of a generic two-qubit
operator.
