From Black Hole to Qubits: Evidence of Fast Scrambling in BMN theory

TL;DR

This paper investigates fast information scrambling in BMN Matrix theory by modeling membrane ripples as qubits and analyzing their entanglement evolution, confirming the logarithmic scrambling timescale predicted by theoretical conjectures.

Contribution

It provides a controlled computational framework to test information scrambling in matrix black holes using qubit models and entanglement dynamics analysis.

Findings

Scrambling timescale scales logarithmically with entropy

Qubit entanglement evolution matches theoretical predictions

Supports the fast scrambling conjecture in a matrix theory context

Abstract

BMN Matrix theory admits vacua in the shape of large spherical membranes. Per- turbing around such vacua, the setup provides for a controlled computational frame- work for testing information evolution in Matrix black holes. The theory realizes excitations in the supergravity multiplet as qubits. These qubits are coupled to matrix degrees of freedom that describe deformations of the spherical shape of the membrane. Arranging the ripples on the membrane into a heat bath, we use the qubit system as a probe and compute the associated Feynman-Vernon density matrix at one loop order. This allows us to trace the evolution of entanglement in the system and extract the characteristic scrambling timescale. We find that our numerical analysis is consistent with this time scaling logarithmically with the entropy of the qubit system, in tune with suggestions by Sekino and Susskind.