Lecture 9: The Monogamy Paradox
The monogamy paradox can be stated very simply. If the black hole horizon is smooth, degrees of freedom across the horizon must be entangled with each other. On the other hand, general results from quantum information imply that, for an old black hole, modes near the horizon must be entangled with the early radiation emitted by the black hole. This is a paradox because it violates the monogamy of entanglement.
The monogamy paradox was initially framed by Mathur using the von Neumann entropy, and then elaborated by AMPS.
The version we discussed in this lecture utilized CHSH correlators. This has some advantages because CHSH correlators are free of ultraviolet divergences and so their use allows us to focus on the essential physics without having to worry about how to define the von Neumann entropy in gravity.
The monogamy paradox differs from the original version of the information paradox because it makes essential reference to the black-hole interior. Moreover, the violation of the monogamy of entanglement is at O(1) and so it appears that small corrections will be insufficient to resolve this paradox.
