We investigate the interplay between coherent gauge-mediated mixingand decoherence in a minimal bipartite channel model using an opera-tional admissibility distance to product structure. The construction ex-tends previous resource-theoretic formulations of channel-level dynamicalnonlocality by introducing an interleaved open evolution on an auxiliarygauge degree of freedom. Crucially, trace-preserving noise applied only af-ter a full unitary leaves the reduced dynamics invariant; therefore decoher-ence must act during coherent mixing in order to influence channel-leveldeviation.Using a Trotterized interleaving of unitary mixing and gauge dephas-ing, we compute the diamond-norm distance δPROD from product channelsacross the (g, γϕ) parameter plane. The resulting atlas exhibits strict γϕ-invariance at zero mixing, weak sensitivity in the perturbative regime, andnonlinear amplification of dynamical nonlocal deviation for sufficientlylarge mixing and decoherence rates. Rather than a sharp phase bound-ary, the curvature–loss ratio Γ = g2/(κγϕ) emerges as an organizing scalegoverning a smooth crossover between regimes.These results provide a channel-level operational refinement of curvature–coherence balance intuitions in non-Abelian coherence field models andfurnish a tolerance-aware framework for analyzing persistence of entan-gling capability under structured decoherence. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
We investigate the interplay between coherent gauge-mediated mixingand decoherence in a minimal bipartite channel model using an opera-tional admissibility distance to product structure. The construction ex-tends previous resource-theoretic formulations of channel-level dynamicalnonlocality by introducing an interleaved open evolution on an auxiliarygauge degree of freedom. Crucially, trace-preserving noise applied only af-ter a full unitary leaves the reduced dynamics invariant; therefore decoher-ence must act during coherent mixing in order to influence channel-leveldeviation.Using a Trotterized interleaving of unitary mixing and gauge dephas-ing, we compute the diamond-norm distance δPROD from product channelsacross the (g, γϕ) parameter plane. The resulting atlas exhibits strict γϕ-invariance at zero mixing, weak sensitivity in the perturbative regime, andnonlinear amplification of dynamical nonlocal deviation for sufficientlylarge mixing and decoherence rates. Rather than a sharp phase bound-ary, the curvature–loss ratio Γ = g2/(κγϕ) emerges as an organizing scalegoverning a smooth crossover between regimes.These results provide a channel-level operational refinement of curvature–coherence balance intuitions in non-Abelian coherence field models andfurnish a tolerance-aware framework for analyzing persistence of entan-gling capability under structured decoherence. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
We construct a minimal non-Abelian coherence field theory (NACFT) that unifies curvature-mediated coherent exchange and open-system dephasing in multi-centre quantum systems.Starting from an SU(2) gauge structure acting on a coherence doublet, we derive a dimen-sionless order parameter Σ directly from gauge-invariant curvature density and dephasing scalevia covariant coarse-graining. The curvature–coherence balance condition g2 = κγϕ emerges asthe stationary curvature–loss closure of the theory. We prove that SU(2) is the minimal non-Abelian completion capable of representing irreducible dual-channel coherence mixing, and weidentify necessary and sufficient conditions under which extension to SU(3) becomes required.Finally, we show that a Hessian metric formulation arises as a controlled geometric reduction,providing a coordinate-independent classification of coherence corridors, collapse regimes, andreactivation branches. All constructions remain within standard quantum mechanics and mini-mal open-system dynamics. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Operational resource theories of quantum channels require measuresthat quantify intrinsic dynamical structure independently of particularinput states or simulation protocols. We introduce admissibility distance,defined as the diamond-norm distance from a bipartite quantum channelto the free set of locally implementable product channels, and developit as a resource monotone for channel-level dynamical nonlocality. Weprove that the measure is faithful, monotone under local superchannels,and subadditive under both sequential composition and tensor products,providing a compositional operational framework for quantifying deviationfrom local dynamics.To calibrate the framework, we analyse an exactly solvable two-qubitentangling family, recovering the analytical diamond distance in the noiseless limit and deriving rigorous contraction bounds under local unital noise,including depolarising channels, before extending the construction to arbitrary finite-dimensional systems through induced trace-norm contractionon the traceless operator subspace.As an illustrative application, we implement admissibility distance forsimulated Atomic Frequency Comb (AFC) retrieval channels, validatingthe numerical implementation against identity, depolarising and phasedamping benchmarks before applying it to structured retrieval noise. Theresulting numerical experiments indicate that admissibility distance responds substantially more strongly to small structured perturbations thanconventional state-fidelity diagnostics within the benchmark considered,suggesting its potential utility as an operational early-warning metric forquantum-memory benchmarking.Unlike state-based quantities such as entangling power or Choi-stateentanglement, admissibility distance measures the operational separation ofa quantum channel from locally implementable dynamics themselves. Theresulting framework provides a mathematically controlled and operationallyinterpretable geometry for analysing noisy quantum channels and resourcetheoretic aspects of quantum dynamics. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
We introduce an operational notion of admissibility for quantum dy-namics defined as the diamond-norm distance of a physical channel froma restricted class of locally implementable channels. For a two-qubit en-tangling family Uθ = e−iθX⊗X , we prove that the noiseless admissibilitydistance to the identity channel equals 2| sin θ|. Extending to locally de-polarized dynamics Eθ,p = (Dp ⊗ Dp) ◦ Uθ , numerical semidefinite-programevaluation reveals a robust factorization δ(θ, p) ≈ 2 sin θ f (p), with f (p)well-approximated by (1 − βp)α over p ∈ [0, 0.6]. The resulting quantitycaptures channel-level nonlocal capability independently of state-specificoutput correlations, as illustrated by probe states that remain uncor-related despite nonzero admissibility distance. These results provide aminimal operational framework for quantifying dynamical deviation fromlocally admissible processes and establish a tractable testbed for furtheranalytic development. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Einstein’s insight that geometry governs energy and momentum defined the ar-chitecture of physics. Here that principle is extended to coherence itself. TheGated Quantum Resonator (GQR) framework shows that coherent energy trans-fer is governed by a curvature–information lawg2 = κ γϕ, (1)linking coupling strength, geometric curvature, and dephasing rate—an analogueof the energy–curvature–entropy balance in general relativity.We derive this law from a non-Abelian SU(3)coh gauge field that confines co-herence into “coherence-neutral’’ manifolds, the microscopic counterpart of theEinstein–Cartan–Penrose geometric–information framework. Its thermodynamicclosure,δ(g2) = TeffδScoh, (2)mirrors Jacobson’s δQ = T δS, embedding quantum coherence in a unified Einstein–Penrose geometry where curvature, torsion, and information are co-dependent. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
The double-slit experiment and its quantum eraser variants remain central to discussionsof quantum measurement, interference, and which-path distinguishability. Despite the long-standing experimental clarity of these systems, their interpretation is often presented in observer-dependent or information-theoretic terms, leading to persistent conceptual confusion.In this review, we re-examine the double-slit and quantum eraser experiments using ageometry-first perspective in which measurement is treated as a structural process rather thanan epistemic one. Specifically, we frame a measurement event as the opening of a condensa-tion gate that permits an otherwise distributed quantum process to localise irreversibly intoa stable record. Interference persists while no exclusive gate is available; which-path markingintroduces distinct gated exits; and quantum erasure corresponds to the removal of geometricdistinguishability, without invoking retrocausality or observer privilege.This reframing preserves all established experimental results while avoiding collapse postu-lates and knowledge-based interpretations. By emphasising constraint, admissible structure, andirreversible localisation, it offers a mechanistically neutral language for understanding quantumerasure experiments and situates them within a broader class of geometry-conditioned dynamicalsystems. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.
Quantum mechanics permits superposition and interference, yet persistent coherent behavioris rare in practice. Across physical systems, most quantum possibilities decohere rapidly, whilea narrow subset recur, stabilize, and function. This work proposes an interpretive, constraint-based framework in which coherence is governed by geometric and boundary conditions ratherthan by detailed energetic optimization. Without modifying quantum mechanics or quantumfield theory, we examine how two complementary constraints—local phase closure and globalmode suppression—act together to regulate which interference structures persist. Biologicalcatalysis, with particular emphasis on the oxygen-evolving complex, is used as a concrete physicalanchor. A previously unremarked hexagonal interference motif is identified in the oxygen-evolving complex (PDB: 8F4I). Broader implications for transient subatomic excitations arediscussed as downstream consequences of the same governance principles. The framework isoffered as a unifying interpretive synthesis rather than a replacement theory. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.