Efficient Scheme of Experimental Quantifying non-Markovianity in High-Dimension Systems

TL;DR

This paper introduces an efficient method combining experimental data and numerical analysis to quantify non-Markovianity in high-dimensional open quantum systems, overcoming exponential scaling limitations of previous approaches.

Contribution

It presents a scalable approach to measure non-Markovianity in high-dimensional systems, avoiding exponential complexity of existing methods.

Findings

Method scales as N^2 with system dimension, significantly reducing complexity.

Successfully applied to high-dimensional quantum random walk system.

Validated against two-dimensional system benchmark.

Abstract

The non-Markovianity is a prominent concept of the dynamics of the open quantum systems, which is of fundamental importance in quantum mechanics and quantum information. Despite of lots of efforts, the experimentally measuring of non-Markovianity of an open system is still limited to very small systems. Presently, it is still impossible to experimentally quantify the non-Markovianity of high dimension systems with the widely used Breuer-Laine-Piilo (BLP) trace distance measure. In this paper, we propose a method, combining experimental measurements and numerical calculations, that allow quantifying the non-Markovianity of a $N$ dimension system only scaled as $N^2$, successfully avoid the exponential scaling with the dimension of the open system in the current method. After the benchmark with a two-dimension open system, we demonstrate the method in quantifying the non-Markovanity of a high dimension open quantum random walk system.