The Birth and Death of Redundancy in Decoherence and Quantum Darwinism

Ijaz Durrani

Philipp Strasberg

There exist two different paradigms for records in isolated quantum systems: decoherent histories (which determines which past events leave formal records) and quantum Darwinism (which determines which current events get redundantly recorded). Neither one implies the other, and connections between the two are scarcely investigated. We unify quantum Darwinism and decoherent histories based on the insight that only redundant records about past events matter. The resulting framework of past redundancy encompasses quantum Darwinism when applied to events at the current time, and it implies the probability sum rule or decoherence of histories. The Bhattacharyya coefficient (or fidelity) plays an important role to establish this connection. Importantly, various examples show that past redundancy is a more widespread phenomenon than the fine-tuned models necessary for quantum Darwinism suggest. We thus arrive at a richer picture in which redundancy can be caused by mechanisms different from quantum Darwinism (such as macroevents or cascade structures), which emphasizes that redundancy is necessary but not sufficient for objectivity, and which, overall, allows to realistically investigate the question: how generic is redundancy in nature?

Chris Fields

Robin Blume-Kohout, Wojciech Hubert Zurek

Quantum Darwinism--the redundant encoding of information about a decohering system in its environment--was proposed to reconcile the quantum nature of our Universe with apparent classicality. We report the first study of the dynamics of quantum Darwinism in a realistic model of decoherence, quantum Brownian motion. Prepared in a highly squeezed state--a macroscopic superposition--the system leaves records whose redundancy increases rapidly with initial delocalization. Redundancy appears rapidly (on the decoherence time scale) and persists for a long time.

Maximilian Schlosshauer, Arthur I. Fine

Oltan Cankat Riordan

This paper examines the role of Quantum Darwinism in explaining the emergence of classical objectivity within The Many-Worlds Interpretation of quantum mechanics. Decoherence explains why macroscopically distinct alternatives become practically inaccessible to local observers, but it does not by itself explain why multiple observers can independently agree on the same classical state. Quantum Darwinism strengthens this account by describing how information about stable pointer states becomes redundantly encoded in environmental fragments. However, this paper argues that redundancy is necessary for objectivity but not enough to explain objectivity. A simple qubit test model implemented in Qiskit is used to demonstrate redundant environmental coding. The discussion connects this claim to Strong Quantum Darwinism, Spectrum Broadcast Structure, and Quantum Discord, which sharpen the distinction between mere correlation and objective classical records. Finally, this paper proposes phase anti-redundancy as a future direction; While pointer state information becomes locally redundant, cross-branch phase information appears to remain globally encoded and increasingly difficult to recover. This suggests that branch objectivity may require not only redundant classical records, but also the fact that cross-branch phase information is encoded in global correlations rather than in locally accessible environmental fragments.