Quantum Channel Capacity of Traversable Wormhole

Abstract

We formulate the Gao-Jafferis-Wall traversable wormhole protocol as a quantum channel and compute its quantum channel capacity. We show that this capacity is governed by the time derivative of an out-of-time-ordered correlator, hence by operator size growth in the holographic dual, and that its growth is bounded above by the Einstein gravity limit. The channel capacity therefore provides a natural benchmark for quantum simulations of traversable wormholes.

12 pages, 8 figures