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A Geometric Area Bound for Information Transfer Through Semiclassical Traversable Wormholes

Fuat Berkin Altunkaynak, Aslı Tuncer

Abstract

We prove a rigorous geometric bound on the transmission of quantum information through semiclassical traversable wormholes. We initially prove an area theorem showing that the minimal throat surface of a traversable wormhole cannot increase using Raychaudhuri's equation together with the null energy condition for the infalling matter. Then, the max-flow in the bit-thread picture, which corresponds to the initial minimal throat area, is shown to set the upper bound on information transfer. We also discuss two glued HaPPY codes as a toy model for a wormhole.

A Geometric Area Bound for Information Transfer Through Semiclassical Traversable Wormholes

Abstract

We prove a rigorous geometric bound on the transmission of quantum information through semiclassical traversable wormholes. We initially prove an area theorem showing that the minimal throat surface of a traversable wormhole cannot increase using Raychaudhuri's equation together with the null energy condition for the infalling matter. Then, the max-flow in the bit-thread picture, which corresponds to the initial minimal throat area, is shown to set the upper bound on information transfer. We also discuss two glued HaPPY codes as a toy model for a wormhole.
Paper Structure (3 theorems, 27 equations, 1 figure)

This paper contains 3 theorems, 27 equations, 1 figure.

Key Result

Lemma 1

Lemma. Let $\mathcal{N}$ be a null hypersurface generated by affinely parameterized null geodesics with tangent $k^a$, and let $\theta(\lambda)$ be the expansion along $k^a$ on a given generator. Assume that along $\mathcal{N}$ the infalling matter satisfies the null energy condition, and that the congruence has vanishing twist, as is the case for a null hypersurface. If $\theta(\lambda_0)\le 0$

Figures (1)

  • Figure 1: (Color online.)(a) Spatial Cauchy slice ($\Sigma$) with a wormhole whose minimal cross-section is the throat $S_0$, connecting the two asymptotic regions $\mathcal{I}_L$ and $\mathcal{I}_R$. (b) Null congruence on $\mathcal{N}$ with basis vectors $\ell^a$ and $k^a$.

Theorems & Definitions (5)

  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Theorem 2