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

Abstract

In this paper, we critically revisit the Horowitz–Maldacena proposal and its generalization by 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 random state near the singularity. We point out that the unitary matrix introduced in Lloyd’s fidelity calculation depends on initial matter states; hence, his result on the high average fidelity may not represent an almost unitary evolution. In opposition to Lloyd’s conclusion, when we do not include the state-dependent unitary matrix for the fidelity computation, we analytically and numerically confirm that information will almost certainly be lost, because the fidelity will approach zero as the degrees of freedom increase.