<PERSON> and the crank's proposals have problems with them.
Take <PERSON>'s proposal first. Let's say there is an external system which is initially fully entangled with some infalling information. Then, the black hole fully evaporates, and assuming purity, this external system is now fully entangled with the outgoing Hawking radiation. <PERSON>'s assertion is that during intermediate periods before the black hole has fully evaporated, there is some tripartite entanglement between the external system, the Hawking radiation which has already been emitted, and the metric outside which determines the mass, location and velocity of the black hole. This tripartite entanglement means neglecting the external metric, there is no entanglement between the external system and the outgoing Hawking radiation. Well, just after the information has passed through the horizon, there could be a random snap decision by the external system whether to jump into the hole and catch up with the infalling information and check if they are still maximally entangled, or remain outside and collect all the remaining Hawking radiation. It takes a time period of about the Schwarzschild radius before it's no longer possible to catch up with the infalling information, which leaves that as a critical window of time. If he decides to jump in and compare notes, he will find maximal entanglement with the infalling information inside. This would seem to suggest even if he chooses to remain outside, he is still maximally entangled with the information inside. By the monogamy of entanglement, he can't also be correlated at all with anything outside the black hole, and this includes the metric outside. Of course, this is a counterfactual conclusion, and maybe such counterfactual reasoning is inadmissible. But if it fails, it can only be because there is no tensor product structure for the Hilbert space for internal and external black hole states.
The crank's proposal has the following difficulty; suppose there is no black hole initially. A control qubit is set up in the superposition $\frac{1}{\sqrt 2}[|0\rangle +|1\rangle ]$. If its value is zero, don't create a black hole. 43
If it's one, create a black hole. The initial state is $|\psi_i\rangle\otimes \frac{1}{\sqrt 2}[|0\rangle +|1\rangle]$. If there's no black hole, presumably, $\rho_f=1$. If there's a black hole, presumably $\rho_f=\rho_s$ is some positive operator less than the identity operator. So, $\rho_f = |0\rangle\langle 0|+\rho_s\otimes|1\rangle\langle 1|$. So, $\langle \psi_f | = \frac{1}{\sqrt 2} \left[ \langle\psi_i|\otimes\langle 0| + \langle \psi_i|\rho_s \otimes\langle 1|\right]$. Now, measure the relative probabilities for the value of the control qubit. It no longer interacts with the system after determining whether or not to create a black hole. True, we normalize $|\psi_i\rangle\langle \psi_f|$, but that doesn't alter the relative probabilities for getting 1 as opposed to 0. The ratio is given by $\langle \psi_i|\rho_s|\psi_i\rangle/\langle\psi_i|\psi_i\rangle$. In general, this ratio will be less than one. This violates unitarity. One way out is to assume $\rho_s$ actually has some eigenvalues greater than 1. Another way out is to assume time evolution is nonunitary inside the black hole. 66