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We analyze the relationship between entanglement (or geometric) entropy withstatistical mechanical entropy of horizon degrees of freedom when described inthe framework of isolated horizons in loop quantum gravity. We show that, oncethe relevant degrees of freedom are identified, the two notions coincide. Thekey ingredient linking the two notions is the structure of quantum geometry atPlanck scale implied by loop quantum gravity, where correlations between theinside and outside of the black hole are mediated by eigenstates of the horizonarea operator.

Statistical and entanglement entropy for black holes in quantum geometry