Almost certain loss from black holes: critical comments on the black hole final state proposal

In this paper, we critically revisit the Horowitz-Maldacena proposal and its generalization of Lloyd. In the original proposal, as well as in Lloyd's generalization, Hawking radiation involves a pair of maximally entangled quantum states in which the ingoing partner state and the collapsed matter form either a maximally entangled pair or a Schmidt decomposed state near the singularity. However, this cannot be the most generic state if there is an interaction between the collapsing matter and the incoming Hawking radiation. In opposition to Lloyd's conclusion such that information can almost certainly escape from a black hole, we analytically and numerically confirm that information will almost certainly be lost because the fidelity will approach zero as the degrees of freedom increase.