Introduces the coherence-time density operator ρ_K(t) as a spatially integrated, time-resolved threshold observable for quantum gate stability. Central result: a Δ-Gate remains active iff ρ_K(t) ≥ ρ_K,min. Proves Lindblad dephasing recovery in the spatially uniform limit (Proposition 2). Derives explicit collapse threshold for distance-d repetition codes (Proposition 3). Embeds all five companion papers (phase coherence, entangled tunneling, gate channel, Heisenberg-Gate, Omega operator) as projections or limits. Relativistic extension: gate lifetime dilates under Lorentz boosts with frame-invariant threshold condition. Seven falsifiable predictions proposed. Paper VI of VII — theoretical capstone of the Δ-Gate series. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).
Introduces the coherence-time density operator ρ_K(t) as a spatially integrated, time-resolved threshold observable for quantum gate stability. Central result: a Δ-Gate remains active iff ρ_K(t) ≥ ρ_K,min. Proves Lindblad dephasing recovery in the spatially uniform limit (Proposition 2). Derives explicit collapse threshold for distance-d repetition codes (Proposition 3). Embeds all five companion papers (phase coherence, entangled tunneling, gate channel, Heisenberg-Gate, Omega operator) as projections or limits. Relativistic extension: gate lifetime dilates under Lorentz boosts with frame-invariant threshold condition. Seven falsifiable predictions proposed. Paper VI of VII — theoretical capstone of the Δ-Gate series. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).
We introduce a one-parameter quantum channel — the gate channel — that continuously interpolates between unitary evolution (K=0) and projective measurement (K=1) via K(t) = 1 − exp(−Γt). Proof that the continuum limit recovers the GKSL/Lindblad master equation for dephasing exactly. Extensions to pipeline structure, general Kraus operators, and multi-environment coupling. Three falsifiable experimental protocols proposed: double-slit interferometry, NMR spin-echo decay, and polarization-state degradation. Paper II of VII in the Δ-Gate theoretical core. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).
Self-contained, deployable five-stage gate-calibration pipeline for noisy quantum systems Stage 1: Cramér–Rao precision floor with Heisenberg-Gate constraint. Stage 2: AR(1) signal conditioning with Kalman filtering and Huber-robust outlier rejection. Stage 3: four coherence metrics (HBT, relative entropy, percent-coherence, absolute normalized). Stage 4: universal Logit-Gate with closed-form two-parameter calibration (x₅₀, slope s). Stage 5: BKW drift surveillance with traffic-light alerting. Includes worked transmon readout example, default parameter table, gate-composition protocol, and time-crystal scheduling. Platform-agnostic. Paper VII of VII — engineering capstone of the Δ-Gate series. Part of the Δ-Gate Formalism (DOI: 10.5281/zenodo.19103765).
We present the genuine, defensible result of the Δ-Gate program as a tool, not a law: a single soft-threshold operator that makes the character of threshold and decoherence transitions determinable from data. Three things are claimed and no more. First, secured: the Δ-Gate measurement channel embeds exactly into a GKSL/Lindblad dephasing generator, recovering the Born statistics as the diagonal of the decohered state — that is, by decoherence, not collapse. Second, owned and new: a two-Fisher uncertainty relation relating the location-Fisher (entropy-arrow) and the parameter-Fisher (gate-sharpness) of any threshold density. Third, a canonical information-geometric framework (Fisher-information substrate, Fisher–Rao length, the 2D-Ising self-dual invariant, and the fluctuation–dissipation relation) that is correct textbook structure, honestly tagged as found, not produced. From these we assemble a diagnostic toolkit that determines a threshold's dynamical class, bifurcation type, and static-to-dynamic coupling. The limits are explicit; the universality claims of the original program are refuted separately in the companion audit (Paper II).
Gate-Based Thermal Relaxation and the Spatiotemporal Observability Cliff in GHZ States Abstract We investigate the observability lifetimes of Greenberger-Horne-Zeilinger (GHZ) states under thermal relaxation noise applied to quantum gates. Key Findings 1. Gate-Localized Noise Discovery Sanity check at N=1 reveals that thermal relaxation acts only during gate execution, not as continuous idle dephasing This explains why measured lifetimes exceed theoretical predictions by factors of 1.6–2.3 2. Phenomenological Scaling Law We introduce a minimal model: lnt∗(N)=c0−aNp with fitted parameters: Acceleration index: α = p − 1 = 0.322 This explains the pronounced "cliff" between N=3 and N≥4 3. Entanglement Horizon (Quantum Moore's Law) We define an operational entanglement horizon N* where coherence lifetime equals circuit formation time: Noise Reduction Horizon N* Current level 9.54 2× reduction 11.6 4× reduction 13.4 8× reduction 15.0 4. Wall-Clock vs Stopwatch Time The weak scaling (α ≈ 0.34 vs theoretical α = 1) highlights a fundamental distinction: Wall-clock: Continuous dephasing during idle → α ≈ 1 Stopwatch: Gate-localized noise only → α < 1 Methods Platform: Qiskit Aer simulator Parameters: T₁ = 120 μs, T₂ = 12 μs, 4096 shots Range: N = 3–9 qubits, 21 time points (0–32 μs) Statistics: Bootstrap 95% CI, AICc/BIC model selection Companion Paper This work provides the spatial extension of the temporal screening mechanism presented in: Takagi, T. (2025). Falsifiable Predictions for Geometric Mass Origin: Screening Mechanism and Observability Limits. DOI: 10.5281/zenodo.18072929 Together, these establish a unified spatiotemporal observability horizon for quantum systems. Files Included GHZ_paper_PRA_final_with_pheno.tex — LaTeX source (PRA format) GHZ_paper_preview_with_pheno.pdf — Compiled PDF (7 pages) equator_predictions_table.tex — Quantum Moore's law table fig1_final.pdf — Coherence decay curves fig2_final.pdf — Scaling analysis with error bars fig_sanity.pdf — N=1,2,3 sanity check fig_unified_horizon.pdf — Spatiotemporal horizon diagram tstar_final.csv — Raw data for reproducibility Keywords GHZ state, quantum coherence, thermal relaxation, gate-based noise, observability lifetime, entanglement horizon, NISQ, decoherence, quantum-classical transition, quantum Moore's law
ΔC Rupture and Decoherence: Quantum Collapse as Bandwidth Failure in a Stiffened Causal Substrate (v2.0) This paper concludes the six-part ΔC physics series. It extends the dynamic causal substrate model into the quantum regime, proposing a mechanical resolution to the long-standing problem of wavefunction collapse. We present a framework in which quantum collapse is not a spontaneous or observer-driven event, but a deterministic failure mode: the rupture of a finite-bandwidth causal substrate when informational load exceeds structural capacity. Core Results: Bandwidth Saturation: The substrate supports a maximum local update rate, Φ_max, beyond which superposition states can no longer be sustained. Collapse Mechanism: Quantum collapse occurs when total causal load exceeds the local bandwidth limit, triggering a discontinuous substrate rupture. Born Rule Emergence: Collapse probabilities are shown to scale with substrate tension associated with each eigenstate, providing a mechanical derivation of quantum statistics. Stiffness Equation: Incorporates the nonlinear stiffening law ζ(Φ), previously defined in Papers 1–5, now extended to define rupture conditions at the quantum limit. Experimental Validation: We analyze recent results from Aguilar & Lutz (2026), who demonstrated work extraction from quantum heat engines beyond the Carnot limit. We interpret this as empirical support for "Registry Lock" — a causal saturation effect predicted by the ΔC model during entangled state loading. Version 2.0 Updates: Complete formalization of the collapse threshold using substrate stiffness and bandwidth equations Integration of stiffness dynamics across gravitational, inertial, temporal, and quantum domains Empirical connection to 2026 Stuttgart experiments on quantum thermodynamics Series Summary: This work completes the ΔC framework, unifying the geometry of General Relativity with the probabilistic behavior of Quantum Mechanics through a common substrate-based formalism: Paper 1: A Dynamic ΔC Substrate for Gravity and Electromagnetism Paper 2: Δ₀ — The Universal Return Field Paper 3: Gravipressure — Gravity and Time Dilation as Substrate Mechanics Paper 4: The Chronon Field — Inertia and Causal Latency Paper 5: Time Is Not a Dimension — Causal Accumulation in a Discrete Substrate Paper 6: ΔC Rupture and Decoherence — Quantum Collapse DOI References: Paper 1: https://doi.org/10.5281/zenodo.17073364 Paper 2: https://doi.org/10.5281/zenodo.17073638 Paper 3: https://doi.org/10.5281/zenodo.17082227 Paper 4: https://doi.org/10.5281/zenodo.17089747 Paper 5: https://doi.org/10.5281/zenodo.17148920
The quantum measurement problem — why and how a wavefunction in superposition collapses to a definite state upon observation — remains unresolved after a century of quantum mechanics. Existing interpretations (Copenhagen, Many-Worlds, Bohmian mechanics, Decoherence, Relational QM) each address the problem partially, yet none provides a unified physical mechanism grounded in established information-theoretic quantities. This paper introduces Resonant Emergence Theory (RET), a new interpretive framework that identifies wavefunction collapse as a Resonance Event — the moment at which the quantum state of a system achieves sufficient information-theoretic overlap with the Bold Memory (BM) structure of its environment.RET operationalises Bold Memory as the von Neumann entropy S(ρ_env) of an environmental system, Temporary Memory (TM) as the incoming quantum state (density matrix) of the system under observation, and Resonance as quantum fidelity F(ρ_TM, ρ_env). The collapse condition is formally expressed as R(TM, BM_env) × S(ρ_env) ≥ θ_c, where θ_c is a critical information-density threshold. This formulation is shown to be consistent with, and an extension of, the Lindblad master equation and standard decoherence theory, while providing a physical interpretation of why the environment causes wavefunction collapse.Five postulates are presented: superposition as unresolved continuity, measurement as a resonance event (requiring no conscious observer), wave-particle duality as pre- and post-resonance phases, entanglement as shared BM structure (no FTL communication), and quantum coherence as the cost of continuity. Three falsifiable experimental predictions are proposed, including a BM-threshold experiment feasible with current cavity QED technology. A companion interactive simulator (RET Lab v1.0) is publicly available at https://doi.org/10.5281/zenodo.19427072.