Quantum Darwinism as Syndrome Broadcast: A Finite-QEC Reconstruction of Objective Records. Up-to-date first-tranche addition: syndrome-broadcast/QEC measurement bridge, record-first reconstruction, pointer-basis/syndrome fan-out and Landauer reset map; build/render checked locally; no matching public Zenodo record or authenticated draft found. This record is part of the finite-QEC substrate / It-from-Bit publication refresh. 2026-06-21 theorem update: Upgrades the paper from a conceptual finite-QEC bridge to a short theorem paper. The new version proves an approximate spectrum-broadcast/strong-Darwinism theorem for noisy stabilizer syndrome extraction, derives Fano-controlled redundancy thresholds, separates ideal GHZ broadcast as the zero-error corollary, and adds an explicit local-versus-globally-compressed Landauer reset ledger.
Quantum Darwinism as Syndrome Broadcast: A Finite-QEC Reconstruction of Objective Records. Up-to-date first-tranche addition: syndrome-broadcast/QEC measurement bridge, record-first reconstruction, pointer-basis/syndrome fan-out and Landauer reset map; build/render checked locally; no matching public Zenodo record or authenticated draft found. This record is part of the finite-QEC substrate / It-from-Bit publication refresh. 2026-06-21 theorem update: Upgrades the paper from a conceptual finite-QEC bridge to a short theorem paper. The new version proves an approximate spectrum-broadcast/strong-Darwinism theorem for noisy stabilizer syndrome extraction, derives Fano-controlled redundancy thresholds, separates ideal GHZ broadcast as the zero-error corollary, and adds an explicit local-versus-globally-compressed Landauer reset ledger.
Quantum Darwinism (QD) and Spectrum Broadcast Structure (SBS) formalize a mechanism by which many observers can learn the same classical pointer value of a system by measuring different fragments of its environment. Most QD analyses treat the observer as idealized: unlimited access, perfect calibration, and no temporal constraints. This paper introduces an explicit observer quality parameterization and propagates it through redundancy and objectivity statements in a way that remains stable under an explicit ε-SBS trace-distance error model. Our main technical contributions are: (i) a decoder-level, tight (Chernoff-optimal) sample-complexity characterization for the number of environmental fragments needed to infer a pointer value under a calibrated observer model, (ii) a data-processing theorem showing that calibration noise (modeled as a CPTP channel) degrades the quantum Chernoff exponent, and (iii) an ε-robustness theorem upgrading ideal-SBS sample-complexity bounds to approximate-SBS states with additive error control. We ground the formalism in a fully worked open-system example: a central-spin pure-dephasing model whose conditional fragment states can be computed analytically, yielding explicit formulas for the observer parameters (R_O, C_O, τ_O) as functions of couplings, readout noise, and acquisition time. We also highlight a sharp performance gap between collective (coherent) decoding and product-measurement decoding for pure-state records, directly linking quantum memory horizon to redundancy. Finally, to connect this physics formalism to the DLN observer-quality framework, we introduce a three-state stage index q_O ∈ {q_D, q_L, q_N} mapping Dot/Linear/Network stages to memoryless, product, and collective decoding classes. We then prove three dynamical results about observer topology over time: (A) a dynamical redundancy theorem showing that the long-run effective Chernoff exponent depends on the observer's revision topology R_O, with full-cycle revision achieving the adaptive optimum while expand-only revision collapses permanently to the linear baseline; (B) an "inverted sophistication" theorem showing that an unmonitored collective decoder can be strictly worse than optimal product decoding below a critical coherence fraction; and (C) a pointer-accessibility proposition formalizing how the DLN stage determines which pointer distinctions are resolvable from a fixed fragment budget, providing an operational basis for observer-designed control of accessible quantum outcomes.
Objective facts in quantum Darwinism are values recorded redundantly in many independently accessible fragments of the environment. Redundancy does not create additional logical information, so its thermodynamic meaning has remained unclear. We show that it creates an exact work asymmetry between controllers with different access architectures. For a record cloud F and a partition P into blocks that cannot be jointly controlled, the reversible isothermal erasure penalty relative to a global controller is kBT times the partition total correlation. If the source event X is supplied as catalytic classical side information, subtracting the corresponding penalty gives the source-loss law FPT=kBT[∑B∈PI(X:FB)−I(X:F)]. We call this the thermodynamic factuality charge. It ranges from −kBTH(X) for perfect secret sharing to (∣P∣−1)kBTH(X) for perfect broadcast objectivity. Its normalized form defines a thermodynamic record number between 0 and ∣P∣. We derive Landauer--Darwin bounds, endpoint-rigidity certificates, exact growth and partition-refinement laws, spectrum-broadcast saturation, and closed formulas for noisy classical and quantum collision models. The theory does not modify quantum mechanics or posit objective collapse; it identifies the thermodynamic resource generated by redundant records under restricted control.
Quantum error correction (QEC) and Quantum Darwinism describe opposing consequences of system-environment interactions: QEC seeks to preserve logical quantum information, whereas Quantum Darwinism explains the emergence of objective classical information through its proliferation into the environment. Despite their common physical origin, no direct quantitative connection between these paradigms has previously been established. We introduce an exactly solvable block-environment model based on the logical GHZ block of the Shor [[9,1,3]] quantum error-correcting code, collectively coupled to N environment qubits. The logical fidelity, Holevo information, and Darwinistic redundancy are obtained systematically for arbitrary environment size and imperfect recovery efficiency. Eliminating the common decoherence parameter yields an exact tradeoff relating Darwinistic redundancy directly to the post-recovery logical fidelity, demonstrating that the emergence of redundant classical records occurs at the expense of logical quantum information. We further prove a model-independent no-go theorem showing that the logical fidelity exceeds a critical threshold precludes the emergence of Darwinistic redundancy, irrespective of the microscopic Hamiltonian or environment structure. The solvable model saturates this general bound, establishing the first quantitative information-theoretic connection between logical quantum information protection and the emergence of redundant classical records.
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.
Quantum Darwinism describes how a classical, objective world emerges when a system's information is redundantly copied into its environment. Existing theory is largely static: it asks whether a given state already has this objective structure. This paper develops the complementary dynamical picture — how objectivity emerges and why it is stable. It builds a genuine "renormalization group," a physicist's tool for tracking how a system looks as one zooms out, and applies it to the environmental record. The central finding is that objectivity is a fixed point of this zooming-out flow: an objective state stays objective at every scale, and — strikingly — the requirement of scale-invariance forces the records to be genuinely classical. The flow has two stable end-states, an "objective" phase and a scrambled "encoded" phase, separated by a sharp transition at a critical broadcast rate. The paper proves that a natural information measure decreases irreversibly along the flow toward objectivity, giving the emergence of classicality a definite arrow, analogous to celebrated "c-theorems" in the physics of critical phenomena. A known model of the objectivity–scrambling transition is recovered as a special limit. Every quantitative claim is reproduced by self-testing code, and the core theorems are additionally verified by proof-checking software. In short: classicality has a direction. Like heat flowing one way, the world coarse-grains toward objectivity and never back — a c-theorem for the quantum-to-classical transition.
Quantum Darwinism and related objectivity frameworks study how information about a quantum system is redundantly recorded in its environment. This preprint studies a downstream selection problem: when several candidate records coexist, which one is public under a specified access channel? The problem is formulated as access-limited quantum hypothesis testing. The global Chernoff distinguishability of a candidate record is compared with the public Chernoff distinguishability after a declared sequence of completely positive trace-preserving access maps. The main result is a sufficient access-algebra separation mechanism: if a broadcast record has extensive distinguishability inside the public access algebra, while a globally stronger encoded record is hidden from that algebra at subextensive rate, then global information density and public distinguishability density have opposite thermodynamic orderings. This is not a definition of objectivity in the sense of Spectrum Broadcast Structure or Strong Quantum Darwinism; it is an operational separation theorem for a declared public decision problem. The preprint gives a random-linear access-algebra construction and controlled realizations based on code distance, local circuits, operator spreading, and protected Hamiltonian access algebras.