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

Two methods for measuring Bell nonlocality via local unitary invariants of two-qubit systems in Hong-Ou-Mandel interferometers