Cryptographic Censorship
arxiv(2024)
摘要
We formulate and take two large strides towards proving a quantum version of
the weak cosmic censorship conjecture. We first prove "Cryptographic
Censorship": a theorem showing that when the time evolution operator of a
holographic CFT is approximately pseudorandom (or Haar random) on some code
subspace, then there must be an event horizon in the corresponding bulk dual.
This result provides a general condition that guarantees (in finite time) event
horizon formation, with minimal assumptions about the global spacetime
structure. Our theorem relies on an extension of a recent quantum learning
no-go theorem and is proved using new techniques of pseudorandom measure
concentration. To apply this result to cosmic censorship, we separate
singularities into classical, semi-Planckian, and Planckian types. We
illustrate that classical and semi-Planckian singularities are compatible with
approximately pseudorandom CFT time evolution; thus, if such singularities are
indeed approximately pseudorandom, by Cryptographic Censorship, they cannot
exist in the absence of event horizons. This result provides a sufficient
condition guaranteeing that seminal holographic results on quantum chaos and
thermalization, whose general applicability relies on typicality of horizons,
will not be invalidated by the formation of naked singularities in AdS/CFT.
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