
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.
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Taxonomy
TopicsQuantum Mechanics and Applications · advanced mathematical theories · Quantum chaos and dynamical systems
