Probing Quantum Information Scrambling via Local Randomized Measurements

TL;DR

This paper introduces a practical method using local randomized measurements to analyze quantum information scrambling, revealing diverse dynamical behaviors in many-body systems efficiently.

Contribution

It develops an analytical framework for accessible information via Haar-random measurements and demonstrates the effectiveness of classical shadow protocols with local randomized probes.

Findings

AAI reveals different scrambling regimes such as localization and ballistic transport.

Classical shadow protocol efficiently extracts AAI with single-qubit measurements.

Numerical simulations confirm the method's ability to distinguish complex quantum dynamics.

Abstract

In quantum many-body dynamics, locally encoded information typically scrambles across the entire system, becoming inaccessible to local probes. The upper bound of accessible information of local probes can be characterized by the Holevo information via optimal measurement. In this work, we investigate the information dynamics of quantum scrambling utilizing local randomized probes, quantified by the averaged accessible information (AAI). We derive an analytical expression for the AAI under Haar-random measurements and demonstrate that it is a function of purity of local reduced density matrix. Operationally, we employ the classical shadow protocol, using only single-qubit randomized Pauli measurements, to efficiently extract the AAI across extended subsystems. Through numerical simulations across diverse many-body paradigms, we show that the AAI can reveal distinct scrambling behaviors, resolving phenomena that range from dynamical confinement and ballistic transport to persistent scar revivals and many-body localization. This work highlights a pragmatic paradigm shift--from relying on optimal measurements to utilizing randomized local probes--for the characterization of complex quantum information dynamics.