Fast-scrambling conjecture

Establish whether quantum systems with bounded-cluster interactions can scramble information in a time that grows only logarithmically with the number of degrees of freedom, and whether black holes realize the fastest possible scrambling rate.

Background

The paper defines scrambling as the spreading of initially simple operator weight over strings involving a number of degrees of freedom of order the total system size. In all-to-all systems this can occur rapidly, whereas locality introduces spatial propagation and a butterfly velocity.

The notes attribute to Sekino and Susskind the conjecture that the fastest systems scramble in logarithmic time and that black holes are the fastest scramblers. The holographic calculation later reproduces logarithmic scrambling for black holes, but the general maximality claim is presented as a conjecture.