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.
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.
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 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.
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.
Noncommuting generators of evolution impose ordering constraints on dynamical systems,restricting the set of admissible transitions. We introduce an Accessibility–Ordering Invariant(AOI) that captures this admissible ordering structure.Three manifestations of ordering geometry are examined in this work. First, ordered trans-port dynamics in graphene systems generate phase ladders in observables governed by a Flo-quet ordering relation. Second, newly identified Schr¨odinger–Heisenberg divisibility fracture inopen quantum dynamics produces ridge manifolds that obey the same ladder condition. Third,atomic-frequency-comb quantum memories exhibit spectral comb structures whose Fourier dualgenerates temporal ladder recurrence.These systems therefore realize a common ordering geometry expressed in conjugate phasecoordinates. In compact form the resulting ladder relations reduce toΓΛ ≈ nπ, tn = n∆ , n ∈ Z,revealing the dual appearance of phase ladders and Dirac-comb temporalis. 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.
This paper extends the Ontological Totality Functional (OTF) programme into the domain of quantum causal structure. Its central claim is that physical admissibility cannot be exhausted by state-level consistency or dynamical stability alone. It must also constrain the admissibility of causal organization itself. The paper introduces a causal defect functional for higher-order quantum processes and argues that definite causal order can emerge as a limiting case of admissible structure. Working in a finite-dimensional process-matrix setting, the paper defines the causal defect as the trace-norm distance to the set of valid causally separable processes with fixed normalization. It proves that this defect is non-negative, vanishes exactly on the causally separable set, and is convex. A free class of admissible supermaps is then identified: linear maps on processes that preserve validity, preserve causal separability, and are contractive in trace norm. Under these maps, the causal defect is monotone. An exact dual operational characterization is established: the causal defect equals the maximal bounded-test advantage over the causally separable set for Hermitian tests of bounded operator norm. In this sense, bounded causal witnesses arise as certified lower-bound functionals for admissibility. To connect the formalism to concrete physical scenarios, the paper studies a dephased-switch family W_eta = W_diag + eta X, where W_diag is causally separable and X encodes interference between orders. For this family, the defect is bounded above linearly in |eta|, while a witness with positive overlap on X yields a matching linear lower bound. As eta tends to zero, the process approaches definite-order admissibility. Within the OTF series, this paper functions as a frontier extension. Paper I introduced physical admissibility mathematically, Paper II studied admissibility in a tensor-cosmology channel, and Paper III interpreted admissibility ontologically. Paper IV shows that the same programme can be pushed into higher-order causal structure, where admissibility constrains not only which states and channels are physically stable but also which causal architectures can count as physically realized. Companion records in the OTF series:OTF I — DOI: 10.5281/zenodo.19068375OTF II — DOI: 10.5281/zenodo.19075284OTF Master Edition — DOI: 10.5281/zenodo.19077303
Cavity-enhanced rare-earth-ion-doped atomic frequency comb (AFC) memoriesexhibit robustness limits not fully captured by peak efficiency or first-order dispersion analysis.We identify a dimensionless ridge-drift ratio that governs tolerance collapse in contrast–bandwidthparameter space. Using a Kramers–Kronig-consistent susceptibility reconstruction and cavitytransfer model representative of rare-earth-ion crystal platforms, we show that survival probabilityfollows a logistic boundary controlled by the ratio of ridge displacement to local admissiblebandwidth width. This collapse law persists across threshold definitions and cavity finesseregimes and is independent of dominance-exchange branch crossings. The results provide aquantitative tolerance condition for robust design of integrated rare-earth photonic quantummemory devices. 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.