We revisit the “state-dependence” of the map that we proposed recently between bulk operators in the interior of a large anti–de Sitter black hole and operators in the boundary CFT. By refining recent versions of the information paradox, we show that this feature is necessary for the CFT to successfully describe local physics behind the horizon—not only for single-sided black holes but even in the eternal black hole. We show that state-dependence is invisible to an infalling observer who cannot differentiate these operators from those of ordinary quantum effective field theory. Therefore the infalling observer does not observe any violations of quantum mechanics. We successfully resolve a large class of potential ambiguities in our construction. We analyze states where the CFT is entangled with another system and show that the $\mathrm{ER}=\mathrm{EPR}$ conjecture emerges from our construction in a natural and precise form. We comment on the possible semiclassical origins of state-dependence.

• Received 9 May 2015

DOI:https://doi.org/10.1103/PhysRevD.93.084049

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Published by the American Physical Society