Objectivity (or lack there of): a comparison between predictions of quantum Darwinism and spectrum broadcast structure

TL;DR

This study compares quantum Darwinism and spectrum broadcast structure in a quantum system, revealing discrepancies in their predictions of objectivity and the nature of information, using a novel environment partitioning method.

Contribution

It introduces a new partial trace method for environment partitioning and compares its predictions with existing methods in analyzing quantum objectivity frameworks.

Findings

Quantum Darwinism can emerge without spectrum broadcast structure.

Most mutual information between system and environment is quantum in nature.

Discrepancies exist between quantum Darwinism and spectrum broadcast predictions.

Abstract

Quantum Darwinism and spectrum broadcast structure describe the emergence of objectivity in quantum systems. However, it is unclear whether these two frameworks lead to consistent predictions on the objectivity of the state of a quantum system in a given scenario. In this paper, we jointly investigate quantum Darwinism and spectrum broadcasting, as well as the subdivision of quantum Darwinism into accessible information and quantum discord, in a two-level system interacting with an $N$-level environment via a random matrix coupling. We propose a novel partial trace method to suitably and consistently partition the effective $N$-level environment, and compare the predictions with those obtained using the partitioning method proposed by Perez [Phys. Rev. A 81, 052326 (2010)]. We find that Quantum Darwinism can apparently emerge under the Perez trace even when spectrum broadcast structure does not emerge, and the majority of the quantum mutual information between system and environment fractions is in fact quantum in nature. This work therefore shows there can be discrepancies between quantum Darwinism, and the nature of information and spectrum broadcast structure.