The meaning of redundancy and consensus in quantum objectivity

TL;DR

This paper clarifies the distinct roles of redundancy and consensus in quantum objectivity, showing how different frameworks measure these features and highlighting their implications for understanding the quantum-to-classical transition.

Contribution

It distinguishes between redundancy and consensus in quantum objectivity, linking them to spectrum broadcast structure and quantum Darwinism, and analyzes states with nonlocal information encoding.

Findings

Redundancy and consensus are distinct, related but separate features.

Spectrum broadcast structure measures redundancy; quantum Darwinism measures consensus.

Nonlocal information encoding can cause a divergence between redundancy and consensus.

Abstract

While the terms "redundancy" and "consensus" are often used as synonyms in the context of quantum objectivity, we show here that these should be understood as two related but distinct notions, that quantify different features of the quantum-to-classical transition. We show that the two main frameworks used to measure quantum objectivity, namely spectrum broadcast structure and quantum Darwinism, are best suited to quantify redundancy and consensus, respectively. Furthermore, by analyzing explicit examples of states with nonlocally encoded information, we highlight the potentially stark difference between the degrees of redundancy and consensus. In particular, this causes a break in the hierarchical relations between spectrum broadcast structure and quantum Darwinism. Our framework provides a new perspective to interpret known and future results in the context of quantum objectivity, paving the way for a deeper understanding of the emergence of classicality from the quantum realm.