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The exotic braiding of anyons is certainly the most tantalizing aspect of fractional quantum Hall states. Although braiding is usually thought as a two-dimensional adiabatic manipulation, the braiding phase can also be captured in one dimension in an out-of-equilibrium setting. We discuss here to what extend a beam splitter reveals the braiding phase when excited with voltage or current pulses. We identify two main physical mechanisms that govern the sign and the size of the output cross-correlations: the non-linearity, characterized by the tunneling exponent, and the presence of holes in the incoming beams, related to the braiding phase. We show how the incoming signals form an environment for the beam splitter (akin to the dynamical Coulomb blockade effect) and thus interpret the mixing not as a collision of particles, but as a collision or interference of waves. We illustrate the physical picture with various examples of excitations for integer and fractional Hall states and show the emergence of genuine antibunching statistics when mixing dense voltage pulses.