Complementarity and the unitarity of the black hole Smatrix
Abstract
Recently, Akers et al. proposed a nonisometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole Smatrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the Smatrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the Smatrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the Smatrix of an evaporating black hole has polynomial computational complexity.
 Publication:

Journal of High Energy Physics
 Pub Date:
 March 2023
 DOI:
 10.1007/JHEP02(2023)233
 arXiv:
 arXiv:2212.00194
 Bibcode:
 2023JHEP...02..233K
 Keywords:

 Black Holes;
 Models of Quantum Gravity;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 39 pages, 92 figures, minor changes, published version