Phase-transition-like behavior in information retrieval of a quantum scrambled random circuit system

TL;DR

This paper investigates phase-transition-like behavior in quantum information scrambling within a chaotic system, revealing sharp changes in information recoverability using Holevo and coherent information measures.

Contribution

It introduces a novel analysis of quantum scrambling dynamics showing phase transitions using Holevo and coherent information in random quantum circuits.

Findings

Information cannot be recovered from less than half the system size.

A sharp increase in stored classical information occurs after surpassing half the system size.

Quantum information scrambling exhibits phase-transition-like behavior near critical points.

Abstract

Information in a chaotic quantum system will scramble across the system, preventing any local measurement from reconstructing it. The scrambling dynamics is key to understanding a wide range of quantum many-body systems. Here we use Holevo information to quantify the scrambling dynamics, which shows a phase-transition-like behavior. When applying long random Clifford circuits to a large system, no information can be recovered from a subsystem of less than half the system size. When exceeding half the system size, the amount of stored information grows by two bits of classical information per qubit until saturation through another sharp unanalytical change. We also study critical behavior near the transition points. Finally, we use coherent information to quantify the scrambling of quantum information in the system, which shows similar phase-transition-like behavior.