Scrambling with Matrix Black Holes

TL;DR

This paper investigates the scrambling properties of black holes within Matrix theory, providing evidence that they act as fast scramblers by modeling their dynamics as complex quantum circuits.

Contribution

It introduces a concrete test bed for quantum gravity in Matrix theory and demonstrates that black hole dynamics resemble Brownian quantum circuits, supporting the fast scrambling conjecture.

Findings

Black hole systems in Matrix theory behave like Brownian quantum circuits.

Evidence suggests black holes are fast scramblers with logarithmic entanglement growth.

Analysis of the Berenstein-Maldacena-Nastase model confirms similar scrambling behavior.

Abstract

If black holes are not to be dreaded syncs of information but be fully described by unitary evolution, they must scramble in-falling data and eventually leak it through Hawking radiation. Sekino and Susskind have conjectured that black holes are fast scramblers: they generate entanglement at a remarkably efficient rate, with characteristic time scaling logarithmically with the entropy. In this work, we focus on Matrix theory -- M theory in the light-cone frame -- and directly probe the conjecture. We develop a concrete test bed for quantum gravity using the fermionic variables of Matrix theory and show that the problem becomes that of chains of qubits with an intricate network of interactions. We demonstrate that the black hole system evolves much like a Brownian quantum circuit, with strong indications that it is indeed a fast scrambler. We also analyze the Berenstein-Maldacena-Nastase model and reach the same tentative conclusion.