The Speed of Quantum Information Spreading in Chaotic Systems

TL;DR

This paper develops a general theory for quantum information spreading in chaotic many-body systems, defining an information speed that varies with initial entanglement and verifying it in spin chains and holographic models.

Contribution

It introduces a universal formula for quantum information speed based on entanglement density, applicable to both spin chains and AdS/CFT field theories.

Findings

Information speed varies from entanglement speed to butterfly speed.

The formula is validated in quantum spin chains and holographic field theories.

Quantum information can propagate at the information speed with decoding.

Abstract

We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdS-Reissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup.