Quantum error correction has given us a natural language for the emergence of
    spacetime, but the black hole interior poses a challenge for this framework: at
    late times the apparent number of interior degrees of freedom in effective
    field theory can vastly exceed the true number of fundamental degrees of
    freedom, so there can be no isometric (i.e. inner-product preserving) encoding
    of the former into the latter. In this paper we explain how quantum error
    correction nonetheless can be used to explain the emergence of the black hole
    interior, via the idea of “non-isometric codes protected by computational
    complexity”. We show that many previous ideas, such as the existence of a large
    number of “null states”, a breakdown of effective field theory for operations
    of exponential complexity, the quantum extremal surface calculation of the Page
    curve, post-selection, “state-dependent/state-specific” operator
    reconstruction, and the “simple entropy” approach to complexity
    coarse-graining, all fit naturally into this framework, and we illustrate all
    of these phenomena simultaneously in a soluble model.

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