In the context of the holographic principle, is the bulk-boundary correspondence due to entanglement? According to the holographic principle, a "bulk" region of D dimensions corresponds to a "boundary" region of D-1 dimensions. In this context, the laws of physics of the bulk can be "encoded" on the boundary, so there is a correspondence between the bulk and the boundary.
My question is:
Does this correspondence arise because there is an entanglement between the bulk region and the boundary? Could they become unentangled, so that the fundamental laws of physics in the boundary could become radically different compared to those in the bulk?
 A: The idea of holography is that the bulk degrees of freedom and the boundary degrees of freedom are the same. They can't be entangled with themselves.
In a simple holographic universe consisting of a single qubit, there is a description of an arbitrary state $α|0\rangle + β|1\rangle$ as a configuration of the bulk, and another description of it as a configuration of the boundary, and you can choose to use either description. There are no states like $(|00\rangle + |11\rangle)/\sqrt2$ because there are no states $|00\rangle$ or $|11\rangle$, only $|0\rangle$ and $|1\rangle$.
Even if the bulk and boundary states were distinct, entanglement couldn't explain their evolving in lockstep, because entangled subsystems don't evolve in lockstep; they just have correlated initial states. You could argue that identical subsystems evolving under identical laws with no nonunitary collapse would remain identical forever, but that would apply just as well to unentangled initial conditions ($|ψ\rangle\otimes|ψ\rangle$).
