Sarfatti Commentary #1
1) "Let's also say that you've ringed it with the ultimate sensor array, including enough telescopes, radio dishes, gravitational wave detectors, and the like to measure every quantum of energy emerging from the system."
The world lines of these detectors is crucial. Detectors on timelike geodesics will not see the same phenomena as COINCIDENT detectors on, e.g. static off-geodesic world lines at a fixed distance outside the black hole horizon because of the Unruh effect.
kT = hg/c
g = proper acceleration magnitude of the detector --> 0 on a timelike geodesic
T = temperature of "real" black body photons
In contrast the COINCIDENT free float weightless detector is in a sea of virtual photons.
So if Bob is firing his rocket engine hovering (static LNIF) at a fixed radial coordinate r from a simple non-rotating black hole of mass M
His radially outward proper acceleration's magnitude is
g(r) = (GM/r^2)(1 - 2GM/c^2r)^-1/2 --> infinity as r --> 2GM/c^2 from outside, so T --> infinity as well.
Of course Bob's rocket engines will quit before Bob can adiabatically approach close to the horizon in a quasi-hovering manner.
On the other hand, Alice is freely falling on a radial geodesic into the black hole. Since her g = 0 she does not see any finite temperature T at all.
However, if Bob gets too close to the horizon and begins to burn up, Alice can catch on fire from Bob if she passes by him too closely.
2) "the monogamy of entanglement' says that no particle can be entangled with more than one thing at a time."
That is not precisely stated. Obviously, one can easily make N-particle entangled states. The "monogamy" seems to pertain to the measure of entanglement (of which there are several) of subsets N' < N that decreases as N --> infinity. Said in other words, roughly, as we increase the number N of maximally entangled particles in a zero entropy pure state, the entropy of the mixed states of entangled subsets will increase (i.e. the degree of entanglement of these subsets will decrease).
Suppose we have a maximally entangled Bell pair state, e.g. the "singlet"
|A,B> = (1/srt2)[|A1>|B0> - |A0>|B1>]
This is a pure state whose von-Neumann pair entropy S(A,B) is zero.
The von-Neumann entropy S is only non-zero for mixed states with classical probabilities pi
S ~ sum over all i of pilogpi
If p1 = 1 all the others pi = 0 and log1 = 0 therefore S = 0.
Treating the entropy S as a necessary, though not sufficient, measure of entanglement we can say that any maximally entangled state must be pure with zero entropy, although not all pure states are even entangled.
To be more precise. Given a complete orthonormal set of base states |i> form the projection operators |i> = (1/sqrt2)[|A1>|B1>|C1> |A0>|B0>|C0>]
Take the partial trace of |ABC>|B1>