Local invariants of braiding quantum gates -- associated link polynomials and entangling power

For a generic n-qubit system, local invariants under the action of SL(2,C)⊗n characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider two-qubit Yang-Baxter operators 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.