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Recently, it was argued that the braiding and statistics of anyons in atwo-dimensional topological phase can be extracted by studying the quantumentanglement of the degenerate ground-states on the torus. This constructioneither required a lattice symmetry (such as $\pi/2$ rotation) or tacitlyassumed that the `minimum entanglement states' (MESs) for two differentbipartitions can be uniquely assigned quasiparticle labels. Here we describe aprocedure to obtain the modular $\mathcal S$ matrix, which encodes the braidingstatistics of anyons, which does not require making any of these assumptions.Our strategy is to compare MESs of three independent entanglement bipartitionsof the torus, which leads to a unique modular $\mathcal S$. This procedure alsoputs strong constraints on the modular $\mathcal T$ and $\mathcal U$ matriceswithout requiring any symmetries, and in certain special cases, completelydetermines it. Our method applies equally to Abelian and non-Abeliantopological phases.

General procedure for determining braiding and statistics of anyons using entanglement interferometry