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arXiv:2509.17775

Functional Information in Quantum Darwinism: An Operational Measure of Objectivity

Arda Batın Tank

Published Oct 7, 2025• 0 citations
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Abstract

Abstract Classical objectivity arises when many independent observers can retrieve the same information about a quantum system without disturbing it. Quantum Darwinism (QD) explains this by treating the environment as a communication channel that redundantly broadcasts information about pointer observables. We develop an operational framework for quantifying this redundancy through the lens of functional information. By introducing a one-sided adequacy criterion based on the Holevo bound, we measure the \emph{abundance} of environment fragments that individually contain nearly all classically accessible pointer information. Using a heterogeneous pure–dephasing model, we sample fragments to extract onset statistics and apply isotonic regression to obtain stable estimates of redundancy and its functional-information counterpart $FI_{QD}=\log_2 R_\delta$. The results reveal a generic onset–plateau structure: redundancy grows rapidly at early times, then saturates at a capacity-limited ceiling, universally across adequacy tolerances. We further connect $FI_{QD}$ to thermodynamic bounds, showing that each additional bit of redundancy implies exponentially increasing minimal heat costs for record stabilization. This approach provides a conservative, model-agnostic measure of emergent classicality, suitable for both theoretical analysis and experimental probing.

DOI
10.21203/rs.3.rs-7781911/v1

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Abstract Classical objectivity arises when many independent observers can retrieve the same information about a quantum system without disturbing it. Quantum Darwinism (QD) explains this by treating the environment as a communication channel that redundantly broadcasts information about pointer observables. We develop an operational framework for quantifying this redundancy through the lens of functional information. By introducing a one-sided adequacy criterion based on the Holevo bound, we measure the \emph{abundance} of environment fragments that individually contain nearly all classically accessible pointer information. Using a heterogeneous pure–dephasing model, we sample fragments to extract onset statistics and apply isotonic regression to obtain stable estimates of redundancy and its functional-information counterpart FIQD=log⁡2RδFI_{QD}=\log_2 R_\deltaFIQD​=log2​Rδ​. The results reveal a generic onset–plateau structure: redundancy grows rapidly at early times, then saturates at a capacity-limited ceiling, universally across adequacy tolerances. We further connect FIQDFI_{QD}FIQD​ to thermodynamic bounds, showing that each additional bit of redundancy implies exponentially increasing minimal heat costs for record stabilization. This approach provides a conservative, model-agnostic measure of emergent classicality, suitable for both theoretical analysis and experimental probing.
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.
A fact of the classical world is public property: many agents can learn it without erasing or revising it. Quantum mechanics offers no such notion, since unknown states cannot be copied and measurement disturbs. This review develops quantum Darwinism’s resolution, which locates classicality in the environment as a broadcast medium carrying independent records of an observable. The framework is assembled in information-theoretic terms: quantum mutual information between system and environment fragments, redundancy at an information deficit, the Holevo quantity separating accessible from total correlation, spectrum broadcast structure as the record-bearing state, and the quantum Chernoff information fixing the rate of accumulation. A proposition proving that spectrum broadcast structure forces the classical plateau fragment by fragment is given. Three media — spin registers, oscillator baths, and scattered photons — are examined, followed by account of a record’s life cycle: formation, degradation under intra-environmental scrambling and information backflow, and counterexamples where decoherence proceeds while no record is deposited. The relation between redundancy and consensus, consistent histories, laboratory evidence, and unresolved problems are treated in closing.
Quantum Darwinism explains classical objectivity through redundant environmental records of a system's pointer states. We show that these records can be established through an intermediate measurement apparatus without direct system--environment interactions. Using exact analytical solutions of quantum circuit models, we compare system monitoring with apparatus monitoring, where the environment interacts only with the apparatus. During encoding, system--apparatus correlations decrease as system--environment correlations grow. Without noise, both models yield identical accessible pointer information and redundancy, while the discord accounts for their different mutual information. The reliability of these records depends on where noise acts. Apparatus bit flips introduce errors shared by successive records, limiting the information recoverable even from the complete environment. In contrast, larger fragments can mitigate independent noise on environment qubits after encoding. Dephasing in the pointer basis leaves the record information unchanged in the model considered. These results extend the description of quantum Darwinism to indirect measurements and clarify the conditions for reliable environmental records.
Quantum Darwinism is a leading framework for explaining how classical reality emerges from a quantum universe—the environment redundantly encodes the pointer state information of quantum systems, enabling multiple independent observers to reach consensus about reality. However, a fundamental question has remained unanswered: Why does the environment possess this capacity for redundant recording? This paper proposes, within the information-potential conversion framework, that the redundant recording mechanism of quantum Darwinism is the physical realization of the information-potential conversion consensus protocol—the environment, acting as the physical medium for information-potential conversion, redundantly encodes system information, providing consistent conversion records for independent information processing units, from which classical reality emerges. Based on this interpretation, three testable quantitative predictions are proposed: (1) In superconducting quantum circuits, when system complexity exceeds a critical threshold, the efficiency of redundant recording should exhibit an abrupt transition—a signal of the information-potential conversion phase transition of the consensus protocol from “quantum critical” to “classically locked”; (2) There should exist a precise linear relationship between functional information and information-potential conversion energy consumption: each additional bit of functional information doubles the minimum heat dissipation required for record stabilization; (3) Consensus strength—the stability of classical reality—should be positively correlated with the number of information processing units participating in the consensus protocol, and a critical number exists at which the consensus phase transition occurs. quantum Darwinism, information-potential conversion, consensus protocol, classical emergence, redundant recording, functional information
This paper proposes a concrete, testable criterion for when quantum events become classical facts. Decoherence alone is insufficient: classicality requires that information about the outcome be redundantly recorded across many independent environmental fragments. Using a spin–environment model, we show that the onset of redundancy can lag behind decoherence, creating a measurable gap between “decohered” and “classically real” regimes. This framework refines quantum Darwinism, preserves unitarity, and explains classical objectivity as a structural property of the environment.
Quantum Darwinism explains the emergence of classical objectivity through redundant environmental encoding of quantum information. Many treatments implicitly treat redundancy as mechanism-agnostic — that is, redundancy is redundancy regardless of how it arises. In this work, I distinguish two channel classes through which environmental records form: passive decoherence, in which information leaks into unstructured environmental degrees of freedom, and active broadcast, in which classical records propagate via selective, high-fan-out channels. I show computationally that these classes produce measurably different redundancy growth rates and record-stability thresholds under comparable noise conditions, and that the distinction is not an artefact of parameter choice but reflects a difference in scaling class: passive (local) channels produce scaling consistent with polynomial spreading times T(N) ~ Nᵝ, while active (non-local) channels produce scaling consistent with logarithmic spreading times T(N) ~ log(N), under the models studied. This separation is consistent with locality constraints formalised by Lieb–Robinson bounds on information propagation in locally-coupled systems. The distinction implies that the route to classicality is not uniquely determined by the quantity of redundancy, but depends on the informational structure of the channel that generates it. This has direct consequences for how we understand irreversibility, the objectivity of measurement outcomes, and the scope of quantum Darwinism as a theory of the classical limit.