The meaning of redundancy and consensus in quantum objectivity

While the terms "redundancy" and "con-sensus" 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 quan-tify different features of the quantum-to -classical transition. We show that the two main frameworks used to measure quan-tum objectivity, namely spectrum broad-cast 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 high-light the potentially stark difference be-tween the degrees of redundancy and con-sensus. In particular, this causes a break in the hierarchical relations between spectrum broadcast structure and quantum Darwin-ism. Our framework provides a new per-spective to interpret known and future re-sults in the context of quantum objectivity, paving the way for a deeper understanding of the emergence of classicality from the quantum realm.