For holographic states, boundary mutual information between regions A and B implies a lower bound on the bulk geodesic distance that grows as log(1/I), forcing divergent separation as I tends to zero.
Jacobson,Entanglement equilibrium and the Einstein equation,Physical Review Letters 116(2016) 201101
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A sharp bound on spacetime distance from quantum entanglement
For holographic states, boundary mutual information between regions A and B implies a lower bound on the bulk geodesic distance that grows as log(1/I), forcing divergent separation as I tends to zero.