Demonstration of quantum Darwinism on quantum computer

It is well known that environmental decoherence is a crucial barrier in realizing various quantum information processing tasks; on the other hand, it plays a pivotal role in explaining how a quantum system’s fragile state leads to a robust classical state. Zurek (Nat Phys 5(3):181–188, 2009) was the first to develop the theory which successfully describes the emergence of classical objectivity of quantum systems using decoherence, introduced by the environment. Here, we consider an n-qubit generalized quantum circuit for the quantum system–environment interaction model, where the first qubit represents the quantum system, and the rest are for the environmental fragments. This quantum circuit is implemented on ibmq_athens and ibmq_16_melbourne for n=2,3,4,5,6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n = 2, 3, 4, 5, 6$$\end{document}. Its accuracy is checked using quantum state tomography and enhanced using the quantum error mitigation procedure. The reconstructed density matrices are used to investigate quantum-classical correlation and the mutual information between the quantum system and the environment. The investigation proves the quantum Darwinism principle when the quantum circuits are executed on the noise-less simulator; however, it shows the unaccountable behavior when implemented on the real quantum devices. The results via the noise-less simulator successfully prove that the environmental fragment size and the interaction strength play a crucial role in the emergence of classicality.