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We demonstrate that the key to realizing arbitrary control over pairs of polarization states of light, i.e., transforming an arbitrarily polarized pair of input states to an arbitrarily polarized pair of output states, is the ability to generate pairs of states with orthogonal polarizations from nonorthogonal pairs of initial states. Then, we develop a new class of non-Hermitian metamaterials, termed complex birefringent metamaterials, which are able to do exactly this. Such materials could facilitate the detection of small polarization changes in scattering experiments as well as enable new polarization multiplexing schemes in communications networks.