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We derive field-theoretic local quantum transport equations which can describe quantum coherence. Our methods are based on Kadanoff--Baym equations derived in the Schwinger--Keldysh closed time path formalism of non-equilibrium quantum field theory. We focus on spatially homogeneous and isotropic systems and mixing fermions with a time-dependent mass and a weak coupling to a thermal plasma. We introduce a new local approximation (LA) method and use it to derive quantum kinetic equations which can describe coherence and also include effects of the spectral width. The method is based on a local ansatz of the collision term. We also improve the earlier coherent quasiparticle approximation (cQPA) by giving a straightforward derivation of the spectral ansatz, a new way of organizing the gradient expansion, and a transparent way to derive the coherence-gradient resummed collision term. In both methods the transport equations can describe flavor coherence and particle--antiparticle coherence, and the related oscillations, of the mixing fermions. In addition to formulating the local equations we apply them to baryogenesis in the early universe. More specifically, we study the details of CP-asymmetry generation in resonant leptogenesis and the evolution of the axial vector current in electroweak baryogenesis (in a time-dependent analogue). We solve the equations numerically, and perform extensive analysis and compare the results to semiclassical (Boltzmann) equations. The results cover known semiclassical effects. We find that dynamical treatment of local quantum coherence is necessary for an accurate description of CP-asymmetry generation. When these details are known they can then be partially incorporated into simpler (e.g. semiclassical) approaches. However, coherent quantum kinetic equations are needed for accurate results across different scenarios or wide parameter ranges.