  We argue that one of the following statements must be true: (a) extensive
violations of quantum information theory's additivity conjectures exist or (b)
there exists a set of `disentangled' black hole microstates that can account
for the entire Bekenstein-Hawking entropy, up to at most a subleading $O(1)$
correction. Possibility (a) would be a significant result in quantum
communication theory, demonstrating that entanglement can enhance the ability
to transmit information much more than has currently been established. Option
(b) would provide new insight into the microphysics of black holes. In
particular, the disentangled microstates would have to have nontrivial
structure at or outside the black hole horizon, assuming the validity of the
quantum extremal surface prescription for calculating entanglement entropy in
AdS/CFT.
