  We describe a direct method to experimentally determine local two-qubit
invariants by performing interferometric measurements on multiple copies of a
given two-qubit state. We use this framework to analyze two different kinds of
two-qubit invariants of Makhlin and Jing et. al. These invariants allow to
fully reconstruct any two-qubit state up to local unitaries. We demonstrate
that measuring 3 invariants is sufficient to find, e.g., the optimal Bell
inequality violation. These invariants can be measured with local or nonlocal
measurements. We show that the nonlocal strategy that follows from Makhlin's
invariants is more resource-efficient than local strategy following from the
invariants of Jing et al. To measure all of the Makhlin's invariants directly
one needs to use both two-qubit singlet and three-qubit W-state projections on
multiple copies of the two-qubit state. This problem is equivalent to a
cordinate system handness measurement. We demonstrate that these 3-qubit
measurements can be performed by utilizing Hong-Ou-Mandel interference which
gives significant speedup in comparison to the classical handness measurement.
Finally, we point to potential application of our results in quantum secret
sharing.
