Replica wormhole and island incompatibility with monogamy of entanglement

TL;DR

The work challenges the claim that replica-wormhole and island-based approaches can reproduce the Page curve purely within standard quantum mechanics and semiclassical gravity by arguing that these methods implicitly invoke non-monogamous entanglement or extra-physics structures. It analyzes the replica-wormhole toy model, highlighting the role of the $e^{-S_0/2}$ term and ensemble averaging in producing a Page-curve-like entropy while showing this is incompatible with strict monogamy as $n\to1$. It also scrutinizes the island formula and its holographic interpretation, noting that the required non-classical connections between interior and radiation would violate monogamy unless new physics is admitted. The paper thus emphasizes that current gravity/holography-based Page-curve constructions likely encode novel physics near black hole horizons, prompting careful interpretation of their implications for the information paradox.

Abstract

We argue that the `island conjecture' and the replica wormhole derivation of the Page curve break monogamy of entanglement through allowing black hole interior states to be non-classically correlated while also pairwise entangled with radiation states. The reason is that quantum degrees of freedom (present in any half of a Hawking pair) cannot all be identified with the environment at semi-classical pair production, and can only be fixed relative to a subsystem, as required for the Page curve, by correlations equivalent to entanglement - regardless of what those correlations are attributed to. This implies that the recent gravity (replica wormhole) and holographic (island conjecture) derivations of the Page curve entail new physics not yet properly taken into account.