Monogamous Entanglement Cheats at the Price of Complexity

Quantum entanglement is monogamous: a system cannot be maximally entangled with multiple partners. Yet thought experiments in gravitational contexts, notably the Hayden-Preskill protocol, appear to challenge this rule. We argue that the illusion of polygamy arises from neglecting the operational cost of decoding. Redistributing entanglement requires teleportation-like operations so computationally demanding that they have gravitational consequences. Entanglement can only “cheat” through complex operations whose backreaction is unavoidable: they may displace the event horizon, render a wormhole traversable, or induce more drastic changes in the spacetime geometry.