We present the results of a study of various notions of entanglement entropy for quantum Hall states. We give analytic and numerical calculations of bipartite entanglement entropy with orbital partitioning, for the Laughlin and Moore-Read states. For the m=3 Laughlin state we extract the topological entanglement entropy as defined by Kitaev-Preskill and Levin-Wen. Studying the entanglement of a subset of the particles with the rest, we establish rigorous upper bounds for the associated entropy.
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