Fast Scramblers

TL;DR

Sekino and Susskind propose a universal logarithmic bound on information scrambling in large quantum systems with bounded interactions, and argue that black holes, Matrix theory, and AdS/CFT realize fast scrambling that saturates this bound. They corroborate the bound with concrete models: random quantum circuits (log N scrambling), D0-brane black holes in Matrix theory, and AdS/CFT constructions, all yielding scrambling times that grow like the inverse temperature multiplied by a constant times the logarithm of the number of degrees of freedom. The Hayden–Preskill thought experiment is central, showing that information retrieval can occur on the scrambling timescale, thus preserving black hole complementarity without observable cloning. The results unify quantum information theory with string-theoretic black holes and suggest gravity enables ultra-fast, non-local scrambling far beyond conventional many-body diffusion.

Abstract

We consider the problem of how fast a quantum system can scramble (thermalize) information, given that the interactions are between bounded clusters of degrees of freedom; pairwise interactions would be an example. Based on previous work, we conjecture: 1) The most rapid scramblers take a time logarithmic in the number of degrees of freedom. 2) Matrix quantum mechanics (systems whose degrees of freedom are n by n matrices) saturate the bound. 3) Black holes are the fastest scramblers in nature. The conjectures are based on two sources, one from quantum information theory, and the other from the study of black holes in String Theory.

Figures (1)

• Figure 1: A thought experiment in which Bob observes quantum cloning.