Fast Scramblers

TL;DR

This paper investigates the speed limits of quantum information scrambling in systems with bounded interactions, proposing that black holes and matrix models are the fastest scramblers, with a conjecture that scrambling time scales logarithmically with system size.

Contribution

It introduces conjectures on the fundamental limits of quantum scrambling speed, linking quantum information theory and black hole physics.

Findings

Black holes are the fastest scramblers in nature.

Scrambling time scales logarithmically with the number of degrees of freedom.

Matrix quantum mechanics saturates the proposed bound.

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.