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The information loss paradox associated with black hole Hawking evaporationis an unresolved problem in modern theoretical physics. In this paper, werevisit the entanglement entropy via the Euclidean path integral (EPI) of thequantum state and allow for the branching of semi-classical histories along theLorentzian evolution. We posit that there exist at least two histories thatcontribute to EPI, where one is an information-losing history while the otheris information-preserving. At early times, the former dominates EPI, while atlate times the latter becomes dominant. By so doing we recover the essence ofthe Page curve and thus the unitarity, albeit with the turning point, i.e., thePage time, much shifted toward the late time. One implication of this modifiedPage curve is that the entropy bound may thus be violated. We comment on thesimilarity and difference between our approach and that of the replicawormholes and the island conjecture.

Solving information loss paradox via Euclidean path integral