1Università degli Studi di Palermo, Dipartimento di Fisica e Chimica – Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy
2Centre for Quantum Materials and Technologies, School of Mathematics and Physics, Queen’s University Belfast, BT7 1NN, United Kingdom
3NEST, Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, 56127 Pisa, Italy
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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.
Featured image: If the information about the system is encoded into the correlations between different environmental constituents, observers can extract it only by measuring all the constituents from the same group. This is an example where it is important to distinguish between the concepts of redundancy and consensus.
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