Maity et al. (arXiv:2608.03944, 2026) proved a tight no-go theorem: QEC and Quantum Darwinism cannot coexist above F_L > 0.874. We audit this through Ostrowski's lens on Bruhat-Tits tree code spaces. v1.9 corrects a red-team finding: the v1.8 text conflated the full-environment theorem boundary (0.874, place-invariant) with the per-fragment model boundary (~0.80, shifted by the single-qubit fragment criterion). The no-go theorem is satisfied (chi(E)=H2(F_bare), R=0 above 0.874); the per-fragment first-redundancy boundary is at ~0.80, shifted below the threshold; the (0.80, 0.874) window is the forbidden-window artifact (alpha-sweep null, reported honestly). Three results: quantization confirmed, N_eff reduction confirmed, disciplined null result on the fidelity-resolved staircase.
Maity et al. (arXiv:2608.03944, 2026) proved a tight no-go theorem: QEC and Quantum Darwinism cannot coexist above F_L > 0.874. We audit this through Ostrowski's lens on Bruhat-Tits tree code spaces. v1.9 corrects a red-team finding: the v1.8 text conflated the full-environment theorem boundary (0.874, place-invariant) with the per-fragment model boundary (~0.80, shifted by the single-qubit fragment criterion). The no-go theorem is satisfied (chi(E)=H2(F_bare), R=0 above 0.874); the per-fragment first-redundancy boundary is at ~0.80, shifted below the threshold; the (0.80, 0.874) window is the forbidden-window artifact (alpha-sweep null, reported honestly). Three results: quantization confirmed, N_eff reduction confirmed, disciplined null result on the fidelity-resolved staircase.
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.
A 20-chapter beginner's guide to quantum computing that starts with an honest question — why don't we have quantum computers yet? The guide teaches the standard curriculum accurately, explains why the standard approach faces a thermodynamic wall (a 20,000-fold cooling gap that is Carnot-limited), and introduces the ultrametric alternative: passive geometric fault tolerance on Bruhat-Tits trees, with DOI-registered evidence, computationally validated error thresholds 75 times higher than surface codes, and three falsifiable predictions. This is the v1.2 edition (August 2026). Five quantitative statements from the May 2026 edition are corrected, each verified by an independent computation deposited with this record (artifacts/verification/verify_guide_claims.py, 35 checks, all passing; see Appendix B). Appendix A records the research program's progress since May 2026, including a trapped-ion falsifiability register, an audit of a 2026 no-go theorem on quantum error correction and quantum Darwinism, and the program's own correction on prime-valuation readings of quantum codes. This deposit includes the complete source set: manuscript, HTML, PDF, references (BibTeX), citation audit, project plan, license, and verification artifacts. v1.2.1 (August 2026): post-publication audit corrections. Chapter 20's summary now lists seven open problems (including the QEC–Darwinism tradeoff); the LHC temperature comparison is marked approximate (95×, rounded); Appendix A correction #5 completed; the citation audit's internal-reference count corrected; open problem 7 carries its numeric bound (F_L > 0.874). No quantitative claims changed. v1.2.2 (August 2026): deposit-file corrections. LICENSE now contains the full CC BY 4.0 International legal code, and README.md is the deposit manifest (a project-blueprint README was attached in v1.2.1 by an automation error). No content changes.
According to Quantum Darwinism, system-environment interactions both einselect particular system properties and encode them redundantly in many independent subsets of the environment, called fragments. This redundancy implies that an observer can recover the einselected information by accessing just one such fragment. However, the protocol by which such reconstruction should occur is often left unspecified. Considering a system Γ interacting with a multipartite environment Ξ, we investigate whether, and under what conditions, the einselected state of Γ can be recovered from environmental fragments using the Petz recovery map. We show that the fidelity between the system's initial state and the state reconstructed via Petz recovery develops a plateau as a function of the fragment size. Our results are supported by both analytical arguments and numerical simulations of large but tractable models.
What does a rising redundancy curve actually prove? This deposit accompanies “Raw-Fragment Benchmarking for Redundancy Tests in Quantum Darwinism and Spectrum Broadcast Structure,” a paper built around a practical but often hidden problem in tests of quantum objectivity. Aggregate mutual-information curves can show that information grows with fragment size, but they do not reveal whether independent fragments really carry accessible, mutually consistent records of the same pointer variable. The missing evidence lives one level lower: in the raw, shot-indexed fragment records. The paper turns that gap into a reproducible benchmark. Starting from a fixed synthetic binary pointer-copy model with 100,000 shots and eight heterogeneous fragments, it asks what a raw-fragment evidence package should expose before redundancy, consensus, or Spectrum Broadcast Structure-style objectivity is inferred. The analysis enumerates all fragment subsets, separates mean-over-subsets and all-subsets threshold crossings, measures fragment disagreement, reproduces analytic binary-channel threshold maps, applies coupling-breaking negative controls, and stress-tests the result against hidden common-mode correlated errors. The resulting picture is sharper than an aggregate curve. In the baseline model, the 0.9 information-fraction threshold is crossed at subset size m=3 under the mean criterion, but only at m=4 under the stricter all-subsets criterion. Negative controls remain below threshold, while a hidden common-mode flip exposes the main fragility axis: many agreeing fragments can still fail as evidence for independent records if they share the same unobserved error source. The attached PDF gives the manuscript-level argument and results. The arXiv source package supports manuscript reproduction, and the ancillary benchmark archive contains the synthetic raw-shot data, subset diagnostics, disagreement tables, threshold maps, negative-control outputs, common-mode sensitivity maps, figures, scripts, manifests, and checksums. The scope is deliberately bounded. This is a synthetic/model-level benchmark and reproducibility package, not an experimental claim that Quantum Darwinism or Spectrum Broadcast Structure objectivity has been observed. Its purpose is to make explicit what future experimental raw-fragment evidence should provide before a plotted redundancy signature is treated as a claim of objective, independently accessible records.
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.
The Bruhat-Tits tree provides an ultrametric substrate for quantum error-correcting codes whose information topology differs from the Archimedean case in ways that may revise the redundancy-fidelity tradeoff established for quantum Darwinism. Two limiting regimes are identified: the large-p limit, in which the ultrametric bound converges to the Archimedean bound, and the deep ultrametric regime of small primes, in which discrete redundancy steps create windows where quantum error correction and classical objectivity may coexist. An experimental protocol is proposed to detect the staircase structure on real quantum processors. All claims are graded with epistemic certainty labels and subjected to an internal red-team audit. Licensed under QNFO Unified License Agreement (QNFO-ULA).