Sensitivity of quantum information to environment perturbations measured with a non-local out-of-time-order correlation function

TL;DR

This paper investigates how quantum information flows and reacts to environment perturbations in open quantum systems, using NMR experiments and a non-local out-of-time-order correlation function to quantify information sharing and sensitivity.

Contribution

It introduces a novel experimental approach to measure system-environment correlations and their sensitivity to perturbations using OTOC in a non-Markovian quantum system.

Findings

OTOC decay exhibits exponential behavior with SEC spread

SEC growth correlates with information flow dynamics

NMR experiments successfully measure quantum information sensitivity

Abstract

In a quantum system coupled with a non-Markovian environment, quantum information may flow out of or in to the system. Measuring quantum information flow and its sensitivity to perturbations is important for a better understanding of open quantum systems and for the implementation of quantum technologies. Information gets shared between a quantum system and its environment by means of system-environment correlations (SECs) that grow during their interaction. We design a nuclear magnetic resonance (NMR) experiment to directly observe the evolution of the SECs and use the second moment of their distribution as a natural metric for quantifying the flow of information. In a second experiment, by accounting for the environment dynamics, we study the sensitivity of the shared quantum information to perturbations in the environment. The metric used in this case is a non-local out-of-time-order correlation function (OTOC). By analyzing the decay of the OTOC as a function of the SEC spread, instead of the evolution time, we are able to demonstrate its exponential behavior.