Fast Pre-scramblers

TL;DR

This paper introduces a measure for quantum information spreading called pre-scrambling, demonstrating that certain models and black holes can rapidly pre-scramble information in logarithmic time.

Contribution

It defines a new measure for quantum pre-scrambling, analyzes a model with enhanced memory capacity, and conjectures about the speed of pre-scrambling relative to scrambling.

Findings

Fast pre-scramblers require logarithmic time in system size.

Enhanced memory capacity model is a fast pre-scrambler.

Pre-scrambling occurs no later than scrambling.

Abstract

We consider the process of diffusion or "pre-scrambling" of information in a quantum system. We define a measure for this spreading or "pre-scrambling" of the wavefunction in terms of a minimum probability threshold for the states in the system's Hilbert space. We illustrate our findings on the example of a prototype model with enhanced memory capacity. We conjecture: (1) The fastest pre-scramblers require a time logarithmic in the number of degrees of freedom. (2) The investigated enhanced memory capacity model is a fast pre-scrambler. (3) (Fast) pre-scrambling occurs not later than (fast) scrambling. (4) Fast scramblers are fast pre-scramblers. (5) Black holes are fast pre-scramblers.