A sharp bound on spacetime distance from quantum entanglement

Ryu-Takayanagi established how boundary entanglement encodes bulk area. We provide the metric counterpart: boundary mutual information imposes a rigorous lower bound on bulk geodesic separation that diverges logarithmically as correlations vanish. A multiscale iteration promotes this local inequality to a global obstruction to bulk connectivity. For parallel strips in AdS$_5$/CFT$_4$, the bound necessitates a quantum resolution of the classical mutual-information transition and fixes the asymptotic growth of geodesic distance.

Source: arXiv:2608.12245v1 - http://arxiv.org/abs/2608.12245v1 PDF: https://arxiv.org/pdf/2608.12245v1 Original Link: http://arxiv.org/abs/2608.12245v1