Version of 08 July 2026: Technically refined preprint incorporating clarifications discovered post-submission. We derive a fundamental upper bound on the number of particles that can sustain quantum coherence in a maximally entangled state from a unified geometric framework in which the observable spacetime 𝓜 is a four-dimensional continuous embedding within a higher-dimensional substratum 𝓐 with quantized information interface. Three derivations—direct application of action quantization, the quantum Cramér-Rao bound, and the quantum capacity of the 𝓜–𝓐 information channel—converge to the canonical form N_crit = n_max ℏ / (2 |λ| |Ψ_max| V₃ τ); these are the same action-quantization constraint expressed in action, metrological, and channel-capacity language: the Cramér-Rao route additionally supplies the metrological (Heisenberg 1/N) reading, but the ceiling N_crit follows in every case from action quantization, not from three independent principles. The bound predicts sharp coherence saturation independent of environmental isolation, distinguishing the framework from standard environmental decoherence. Discriminating signatures include a conjectured distinction between fermionic and bosonic systems, an abrupt knee in decoherence rate scaling at N_crit, and a trade-off N · τ ≤ K_AFT relevant to quantum computation. A natural reinterpretation of dynamical decoupling as embedding trajectory engineering connects the framework to established experimental techniques.
Version of 08 July 2026: Technically refined preprint incorporating clarifications discovered post-submission. We derive a fundamental upper bound on the number of particles that can sustain quantum coherence in a maximally entangled state from a unified geometric framework in which the observable spacetime 𝓜 is a four-dimensional continuous embedding within a higher-dimensional substratum 𝓐 with quantized information interface. Three derivations—direct application of action quantization, the quantum Cramér-Rao bound, and the quantum capacity of the 𝓜–𝓐 information channel—converge to the canonical form N_crit = n_max ℏ / (2 |λ| |Ψ_max| V₃ τ); these are the same action-quantization constraint expressed in action, metrological, and channel-capacity language: the Cramér-Rao route additionally supplies the metrological (Heisenberg 1/N) reading, but the ceiling N_crit follows in every case from action quantization, not from three independent principles. The bound predicts sharp coherence saturation independent of environmental isolation, distinguishing the framework from standard environmental decoherence. Discriminating signatures include a conjectured distinction between fermionic and bosonic systems, an abrupt knee in decoherence rate scaling at N_crit, and a trade-off N · τ ≤ K_AFT relevant to quantum computation. A natural reinterpretation of dynamical decoupling as embedding trajectory engineering connects the framework to established experimental techniques.
The M-A Information Channel: A Quantum-Theoretic Characterization of the Information Interface in Higher-Dimensional Embedding Frameworks
July 8th, 2026: Technical updates following the development of the Absolute Frame Theory. We characterize, in the language of quantum channel theory, the information interface between a four-dimensional observable manifold M and a higher-dimensional substratum A proposed in the Absolute Frame Theory. We show that the routing term of the interaction Lagrangian induces a completely positive trace-preserving map Φ: B(H_M) → B(H_A) whose effective output dimension is fixed by the action quantization axiom. We compute the four standard capacities of this channel—quantum capacity Q, classical capacity C, entanglement-assisted classical capacity C_E, and private classical capacity P—and show that each carries distinct physical interpretation: Q bounds the number of coherent pointers that can be sustained simultaneously, C bounds the rate of classical information transmissible from M to A, C_E − C quantifies the structural cost imposed by the thermodynamic isolation axiom, and P relates to the recoverability of information once transferred. We discuss the framework as a quantum-theoretic instantiation of a multidimensional informational substratum—a notion structurally related to the historical concept of aether but free of the empirical constraints that refuted its classical version. We show that the channel framework yields a natural resolution of the black hole information paradox: information transferred through Φ to the substratum is not destroyed by horizon formation, only made operationally inaccessible to observers confined to M. We discuss connections with holographic frameworks, implications for the macroscopic-classical transition, and the experimental signatures accessible through current quantum information platforms.
This paper examines information stability and collapse across physical scales within the Representational Sufficiency Principle (RSP) framework established in "On the Foundations of Informational Physics" (Kozyra, 2026, Zenodo DOI: 10.5281/zenodo.17783127). I propose that collapse occurs when the minimal algorithmic description length of a state exceeds the maximal representational capacity of the bulk geometry. The criterion is K(ψ) > SBek, where K(ψ) denotes Kolmogorov complexity and SBek = Ac3/4Gℏ represents the holographic entropy bound. This renders collapse geometry-dependent, scale-dependent, and observer-independent. The framework preserves global unitarity through complexity redistribution and requires no modification to quantum mechanics. Three testable predictions follow: (1) calculable mesoscopic thresholds where coherence vanishes independent of environmental decoherence, (2) geometry-dependent collapse rates varying with gravitational potential, and (3) no requirement for non-unitary dynamics. The collapse threshold can be approached not only through particle mass but through controlled entanglement with auxiliary photonic degrees of freedom. This protocol may enable near-term experimental testing using levitated nanoparticles coupled to high-Q microwave cavities, with a calculable prediction for the critical photon number at which interference visibility should decrease independent of environmental decoherence. The criterion applies across scales: protein folding exhibits one-dimensional sequence information projecting onto three-dimensional geometry under configurational constraints; quantum measurement shows superposition collapse when representational capacity saturates; cosmological cycles preserve structural ordering through minimal encoding. The common mechanism is geometric constraint on representational capacity. A probabilistic analysis further demonstrates that life emergence under unbiased initial conditions is effectively impossible in a single cycle, and that cyclic informational heredity is structurally necessary to render it non-negligible — converting the classical improbability argument for design into an affirmative case for cosmic heredity. The framework connects measurement to established bounds from holographic entropy and algorithmic information theory. A unified variational derivation of these results alongside the Einstein field equations is developed in the companion paper "On the Unification of Informational Physics" (Kozyra, 2026, Zenodo DOI: 10.5281/zenodo.18666908).
Preprint: This paper derives quantitative bounds on measurement windows for finite-capacity observers extracting information from decohering quantum systems, extending standard decoherence theory to realistic experimental constraints. Main Result: For Gaussian-Markovian decoherence with exponential information decay I(t) = I₀ exp(-2Γt), bounded-capacity observers lose access to system distinctions when mutual information drops below detection threshold ε, yielding measurement window: τ_c = (1/2Γ) log(α C_A / ε) where Γ is decoherence rate [s⁻¹], C_A is observer capacity [bits] defined via Shannon formula (bandwidth × log₂(SNR) × integration time), ε is detection threshold [bits], and α ~ 0.1-1 is a model-dependent constant from spectral decomposition of environmental information. This establishes logarithmic capacity-scaling: doubling detector quality extends measurement windows by only ~0.35/Γ seconds, implying diminishing returns from capacity improvements. Experimental Predictions: For state-of-the-art circuit QED (superconducting transmon qubits, T₁ = 100 μs, bandwidth Δf = 10 MHz, SNR = 10), the framework predicts τ_c ~ 4-10 μs. Varying bandwidth from 1-30 MHz (capacity C_A ∈ [3, 90] bits) produces measurable Δτ_c ≈ 1.7 μs variation (5-10% of coherence time). Five experimental tests discriminate capacity-scaling from standard decoherence: ∙ Tests 1-3: Verify logarithmic capacity-scaling, inverse rate-dependence, threshold-dependence ∙ Test 4: Multi-observer non-redundancy (at most one narrowband detector succeeds) ∙ Test 5: Capacity-dependent redundancy buildup (primary discriminating signature) Key Contributions: ∙ First quantitative analysis of Zurek's pre-objective phase under explicit finite-resource constraints ∙ Capacity-scaling law connecting Shannon information theory to quantum measurement dynamics ∙ Operational definitions ensuring falsifiability (capacity, threshold, mutual information defined via measurement protocols) ∙ Concrete numerical predictions for three platforms (circuit QED, spin qubits, optomechanics) with resource estimates ∙ Design principle: environmental shielding (linear benefit in τ_c) outperforms detector improvement (logarithmic benefit) when both options available Technical Approach: The bound follows from threshold-crossing analysis of exponential decay with capacity-limited initial information I₀ = α C_A, justified via spectral decomposition of environmental information under flat-spectrum approximation for narrowband observation. All parameters (Γ, C_A, ε) are operationally defined and independently measurable, avoiding circularity. Extensions to non-Markovian dynamics (memory kernels), scrambling systems (black holes, many-body chaos), and non-Gaussian noise (Lévy flights, 1/f noise) are discussed with conjectured scaling laws. Scope: The bound applies specifically to Gaussian-Markovian systems (harmonic oscillators, qubits in dispersive limit, weak continuous measurement with memoryless baths). Circuit QED provides optimal testbed due to tunable Purcell filters (bandwidth control), high coherence times (T₁ > 300 μs achieved), and multiplexed readout infrastructure (5+ independent detectors demonstrated). Validity requires α C_A > ε (initial information exceeds threshold); domain violations occur when capacity too small, threshold too high, or coupling too weak. Relation to Prior Work: Zurek's Quantum Darwinism (2003-2009) explains asymptotic objectivity emergence through environmental redundancy but assumes unbounded observers (C_A → ∞, t → ∞). This work analyzes the complementary finite-resource regime (C_A < ∞, t ~ τ_c), providing first capacity-parameterized bound on pre-objective phase duration. Framework is interpretation-neutral—compatible with Copenhagen, Many-Worlds, Bohmian mechanics, and relational quantum mechanics. Philosophical implications (process ontology, observer-dependent reality, impermanence) are explored but clearly separated from testable predictions. Methods: Open quantum systems theory, Shannon information theory, operational quantum measurement, circuit QED experimental physics, numerical prediction for realistic parameters. Content: Complete 90-page manuscript with axiomatic framework (§2), narrowband observation model (§3), main theorem with proof (§4), numerical predictions (§5), five experimental falsification tests (§6), detailed Quantum Darwinism comparison (§7), extensions and limitations (§8), interpretive options (§9), and honest assessment (§10). Includes 77 references and operational definitions for all information-theoretic quantities. Target Audience: Quantum foundations researchers, experimental quantum physicists (circuit QED, trapped ions, quantum dots), quantum information theorists, philosophers of physics interested in measurement and objectivity.
Standard quantum decoherence theory explains the loss of quantum coherence as arising entirely from the coupling between a system and its external environment. In that framework, the decoherence rate decreases as temperature drops and environmental coupling weakens, vanishing in the ideal limit of absolute zero. This prediction relies on the assumption that time is continuous at the most fundamental scale. We explore the consequences of relaxing that assumption. If physical time possesses a smallest unit τ, then each discrete update of a quantum state necessarily involves at least one irreducible phase refresh. From this we derive a lower bound on the decoherence rate that is independent of any environment: Γ_disc = 1/(2πτ). The bound is intrinsic to the discrete structure of time and cannot be eliminated by cooling or isolating the system. The value of τ is fixed by matching the kinetic term of a discrete U(1) gauge field to the standard continuum theory, yielding τ ≈ 29.7 Planck times. This gives Γ_disc ≈ 3.45 × 10^41 s^{-1}, on the order of the Planck frequency. A crucial difference from standard decoherence theory emerges: while the standard framework permits the decoherence rate to approach zero at absolute zero, the discrete-time framework forbids this convergence absolutely. The two theories thus make mutually exclusive predictions, offering a clear conceptual criterion for experimental distinction. We discuss experimental prospects with full transparency. Current environmental decoherence rates (kHz to GHz) lie many orders of magnitude above Γ_disc, so a direct measurement of the predicted plateau is not feasible with present technology. The falsifiability of the prediction rests on the qualitative, principle-level claim that a strictly zero decoherence rate can never be observed, no matter how perfectly isolated a system becomes. As ultralow-temperature techniques advance, a persistent non-zero decoherence floor would support the discrete-time picture. The paper is part of the Generative Discrete Action Principle series. All derivations leading to Γ_disc > 0 are self-contained and rely only on the three explicitly stated premises of a minimum time step, positive-definite state-update records, and S¹ periodicity of phase. Results borrowed from the broader framework, such as the numerical prefactor that fixes τ, are clearly labeled as citations.
Version: v1.0 DESCRIPTION: We introduce Coherence Field Dynamics (CFD), a theoretical framework that extends holographic quantum gravity by promoting quantum coherence — the off-diagonal density matrix elements — to an independent geometric degree of freedom. While standard holographic frameworks (AdS/CFT, Ryu-Takayanagi) encode bulk geometry through entanglement entropy alone, CFD posits that coherence parameterizes effective bulk depth, complementary to entanglement's encoding of connectivity. The coherence field φ(p,γ) satisfies a wave equation in information-geometric parameter space, generating a Lorentzian metric that degenerates at a critical decoherence threshold γ_c. The framework predicts the existence of such a threshold from geometric stability analysis; its specific numerical value is system-dependent. Connections are established between information geometry, MERA tensor networks, and holographic entropy. The variational principle coupling coherence to an effective gravitational action is presented as an analogue gravity model (c and G are effective parameters), not a claim about physical 4D spacetime. Key results: Theoretical framework: coherence field equation, information-geometric metric, variational principle, and five testable predictionsCompanion experimental work demonstrates a fidelity threshold at γ ≈ 0.535 on IonQ Forte-1 (F = 0.988 baseline, collapse to F ≈ 0 under dephasing) and consistency with the dephasing response on Pasqal FRESNEL_CAN1 QPU (noise ratio 1.13×). These results are consistent with CFD's predicted critical behavior, though they do not uniquely distinguish CFD from standard noise models. The specific threshold value (0.535) is determined by the experimental circuit geometry, not derived from CFD aloneFour predictions remain open and experimentally accessible on current NISQ hardware: coherence-depth complementarity, MERA-decoherence correspondence, coherence-modulated entropy scaling, and hardware demonstration of non-trivial reversibilityThis paper presents the theoretical framework. The detailed experimental protocols and hardware data are reported in the companion publication "Cross-Platform Noise Thresholds in Quantum Teleportation: Trapped-Ion and Neutral-Atom Architectures" (see Related Identifiers).
We derive a testable consequence of the hypothesis that quantum decoherence is subject to a global compression bound. Starting from the bounded compression condition, we show that simultaneous decoherence across multiple channels of a quantum system must satisfy a trade-off relation: the weighted sum of individual decoherence rates is bounded by a maximum determined by the system's energy scale and the quantum channel capacity of the system-environment coupling. We derive this bound from two independent physical principles: the finite quantum channel capacity of the environment as an information sink, and the thermodynamic cost of irreversible decoherence via the Landauer principle. For multi-qubit systems, we predict that the decoherence rate of maximally entangled (GHZ) states saturates for sufficiently large qubit number N, deviating from the linear scaling predicted by standard Lindblad theory. We identify the transition regime between weak and strong system-environment coupling as the natural domain where the bound becomes experimentally accessible, and propose concrete protocols using superconducting qubits, trapped ions, and mesoscopic systems. The predictions are falsifiable and independent of any specific interpretive framework for quantum mechanics.