Dynamics of quantum information scrambling under decoherence effects measured via active spins clusters

TL;DR

This paper develops a model to quantify quantum information scrambling in many-body systems under decoherence, using NMR-inspired experiments and out-of-time-order correlators, revealing how imperfections induce localization effects.

Contribution

The work introduces a new model and analytical expressions for OTOCs that account for experimental imperfections and decoherence in measuring quantum information scrambling.

Findings

Excellent agreement between model predictions and NMR experiments.

Decoherence causes localization of information scrambling.

The model enables quantification of quantum dynamics in large systems.

Abstract

Developing quantum technologies requires the control and understanding of the non-equilibrium dynamics of quantum information in many-body systems. Local information propagates in the system by creating complex correlations known as information scrambling, as this process prevents extracting the information from local measurements. In this work, we develop a model adapted from solid-state NMR methods, to quantify the information scrambling. The scrambling is measured via time-reversal Loschmidt echoes (LE) and Multiple Quantum Coherences experiments that intrinsically contain imperfections. Considering these imperfections, we derive expressions for out-of-time-order correlators (OTOCs) to quantify the observable information scrambling based on measuring the number of active spins where the information was spread. Based on the OTOC expressions, decoherence effects arise naturally by the effects of the nonreverted terms in the LE experiment. Decoherence induces localization of the measurable degree of information scrambling. These effects define a localization cluster size for the observable number of active spins that determines a dynamical equilibrium. We contrast the model's predictions with quantum simulations performed with solid-state NMR experiments, that measure the information scrambling with time-reversal echoes with controlled imperfections. An excellent quantitative agreement is found with the dynamics of quantum information scrambling and its localization effects determined from the experimental data. The presented model and derived OTOCs set tools for quantifying the quantum information dynamics of large quantum systems (more than $10^{4}$ spins) consistent with experimental implementations that intrinsically contain imperfections.