Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The QICT Program: From Gauge-Coded Microscopic Unitary Dynamics to an Audited Micro–Macro Closure

Mohamed Sacha

Published Dec 23, 2025• 0 citations
Publisher

Abstract

We present a self-contained, audit-grade formulation of the Quantum Information Copy-Time (QICT) program as a micro–macro closure framework. The microscopic layer is strictly unitary and localitypreserving (a quantum cellular automaton, QCA), including a gauge-coded code-subspace construction and a continuum Dirac limit as a controlled long-wavelength approximation. The central micro–macro bottleneck is the emergence of diffusion from deterministic unitary dynamics. Rather than overclaiming a resolved theorem where the general problem remains open, we (i) replace informal “fast mixing” language by a structured, measurable spectral criterion in the hydrodynamic sector (SDC), and (ii) provide a quantitative bridge showing how certified second-moment (design-channel) diffusion controls infinite-temperature density correlators whenever a local approximate-design property holds (with explicit error bounds). We supply complementary numerical evidence: exact-unitary diagnostics by ED at L = 12 with an L = 14 cross-check, a max-L certification up to L = 512 at the momentchannel level, including a vanishing ballistic/Drude proxy, and a scalable unitary MPS–TEBD typicality diagnostic with explicit Drude bounds and bond-dimension convergence tests. We then propagate audited parameter intervals through a phenomenological closure map, with an explicit reproducibility contract (JSON, hashes, and PASS/FAIL verifier). All claims are labeled as PROVEN, CERTIFIEDNUMERICAL, EXTERNAL-DATUM, HYPOTHESIS, or CONJECTURE.

DOI
10.20944/preprints202512.2120.v1

Related papers

QICT at Maximum Referee Standard: Formal Dependency Graph, Certified Predicates, and Proof-Only Claims (with Explicit Model Boundaries)

Sacha Mohamed

We present a maximal referee-grade formulation of the Quantum Information Copy Time (QICT) program. All claims are restricted to (i) standard Axioms (locality, stationarity/KMS, conservation), (ii) executable certification predicates, or (iii) Theorems with fully enumerated premises. The key observable is the copy time \( \tau_{\text{copy}} \), defined operationally via Helstrom distinguishability. A certified hydrodynamic-window predicate CHW (constructed from finite-time witnesses and residual tests) gates every micro--macro statement. Under \( \)CHW we derive diffusion and prove the central scaling \( \tau_{\text{copy}} = \Theta\!\left(\sqrt{\chi^{(2)}_{\text{micro}}}\right) \), where \( \chi^{(2)}_{\text{micro}}=\langle \delta Q,\,(-\mathcal{L}_\perp)^{-2}\,\delta Q\rangle_{\mathrm{KM}} \) is a second-moment fast-complement susceptibility. Optional bridges (thermal modular saturation and Higgs-portal matching) are isolated as explicit model Axioms; the "Golden Relation'' is then a Theorem and is non-circular provided an independent \( \tau_{\text{copy}} \) inference NC is satisfied. We include an explicit, dataset-level certification appendix (tables generated from bundled validation outputs), enabling direct audit.

•Jan 9, 2026•0 citations

Quantum Information Copy Time (QICT): Operational Definition, Minimal Locality Bounds, Hydrodynamic Susceptibilities, and a Programmatic Outlook

Sacha Mohamed

We formulate and benchmark an operational timescale—the quantum information copy time—that quantifies how rapidly a localized bias in an initial many-body state becomes remotely certifiable using measurements restricted to a distant receiver region. The definition is intrinsically information-theoretic: for a fixed distinguishability threshold \eta \in (0,1), the copy time \tau_{\mathrm{copy}}(A \to B; \eta) is the earliest time at which the reduced states on B become distinguishable with advantage at least \eta, quantified by the trace distance and equivalently by the optimal Helstrom measurement. We present (i) a minimal theorem that isolates the genuinely nontrivial ingredients—locality, conservation laws, and an explicit receiver-observable class—and (ii) a controlled hydrodynamic closure in which the copy time is governed by a second-moment spectral susceptibility that ties the receiver advantage to the slowest transport mode. We then provide reproducible exact-diagonalization benchmarks in the XXZ chain that (a) extract finite-size transport diagnostics with conservative uncertainty quantification and (b) delineate failure modes in integrable and near-integrable regimes. TEBD/MPS calculations are included only as qualitative cross-checks (Supplementary File S1) and are not used to support asymptotic scaling claims. Finally, we include a brief, clearly separated outlook on how locality-preserving quantum cellular automata (QCA) and code-subspace constraints might shape operational copy-time distances; this material is explicitly conjectural and is not used in any theorem, bound, or numerical claim.

•Feb 2, 2026•0 citations

Quantum Information Copy Time (QICT): Operational Definition, Minimal Locality Bounds, Hydrodynamic Susceptibilities, and a Programmatic Outlook

S Saad Mohamed.

We formulate and benchmark an operational timescale—the quantum information copy time— that quantifies how fast a localized bias in an initial many-body state becomes remotely certifiable by measurements restricted to a distant receiver region. The definition is intrinsically information-theoretic: for a fixed distinguishability threshold η ∈ (0, 1), the copy time τcopy(A → B; η) is the earliest time at which the reduced states on B become distinguishable with advantage at least η, measured by trace distance and equivalently by the optimal Helstrom measurement. We present (i) a minimal theorem that isolates which inputs are genuinely nontrivial (locality, conservation laws, and an explicit receiver observable class), and (ii) a controlled hydrodynamic closure in which the copy time is governed by a second-moment spectral susceptibility that couples the receiver advantage to the slowest transport mode. We then provide reproducible exact-diagonalization benchmarks in the XXZ chain that (a) extract finite-size transport diagnostics with conservative uncertainty quantification and (b) delimit failure modes in integrable and near-integrable regimes. TEBD/MPS calculations are included only as qualitative cross-checks (Supplementary File S1) and are not used to support asymptotic scaling claims. Finally, we situate these results inside the broader QICT program, where locality-preserving quantum cellular automata (QCA) and code-subspace constraints motivate using copy-time distances as primitives for an operational geometry; we keep this outlook explicitly conjectural and separate from the proved/validated statements.

•Jan 6, 2026•0 citations

Primitive Copy Sectors and Diffusive Infrared Closure: A Quantum-Information Copy-Time Criterion

Mohamed Sacha

Abstract We formulate quantum-information copy time (QICT) as a conditional operator-algebraic criterion for diffusive infrared sectors of local quantum dynamical systems. The microscopic input is a physically accessible observable net rather than the full matrix algebra of all microscopic labels. This distinction is used throughout: locality, reversibility and exact charge conservation do not imply primitivity of the dynamical commutant once superselection or operationally inaccessible labels are present. We prove a fragmentation theorem on such observable nets, construct the Kubo-Mori fluctuation Hilbert space under exponential clustering, and state a closed QICT datum consisting of a primitive infrared centre, vanishing Drude projection, a sectorial Kubo-Mori Dirichlet form and absence of singular metric mass. The main theorem is a hydrodynamic Feshbach-Schur criterion: if the Bloch fibre of the effective generator is analytic at the origin and the QICT datum holds, then the isolated scalar copy mode has a diffusive pole with tensor λ(k) = −D ij k i k j + O(|k| 3 ), D ij = D ij bare + χ −1 ⟨Ji,M −1 J j ⟩ KM , M = −QL 0 Q. The criterion is non-empty: an exchange-dephasing quantum Markov sector verifies it on a closed one-density fluctuation sector, with an explicit observable net, stationary state, Bloch fibre, sectoriality and diffusion tensor. Gauge-code terminality and a scalar Higgs-portal benchmark enter only as applications under additional restricted hypotheses. The raw scalar benchmark is excluded by xenon direct-detection limits unless an independently derived copy-code form factor supplies the required suppression.

•May 12, 2026•0 citations

Operational Copy Time and Audited Closure: A Locality–Mixing Separation Diagnostic for Open Quantum Dynamics

Mohamed Sacha

We develop an operational certification framework for micro–macro modeling in local quantum systems. Audited closure is defined as a uniform discrepancy bound between microscopic and surrogate predictions over a declared observable suite on a declared domain of states. A receiver-region copy time τ_copy(η;A→B) is defined as the earliest time at which a finite receiver region B can distinguish—at trace-distance threshold η—a localized perturbation supported on A. Under explicit Lieb–Robinson hypotheses for Hamiltonian or Lindbladian generators, we derive an exponential receiver distinguishability envelope and an explicit time-to-threshold lower bound, including the regime η≥Γ where the threshold is provably never reached and τ_copy=+∞. As an achieved-closure demonstration, we analyze a split-step quantum walk lifted to quasi-free lattice fermions and provide computable dispersion and two-point density audit bounds on a band-limited quasi-free domain. As a signature contribution beyond a repackaging of locality, we prove a locality–mixing separation theorem for primitive Lindbladians with a log-Sobolev (or mixing) rate λ: the receiver distinguishability is bounded by the minimum of a ballistic LR tail and an intrinsic mixing contraction, yielding a measurable crossover time and an operational separation between unitary and dissipative dynamics.

•Jan 6, 2026•0 citations

The Synchronization Latency Principle: Geometric Coherence, Informational Audit, and the Emergence of Inertia and Mass

Mohamed Sacha

We formulate an operational hypothesis—the Synchronization Latency Principle—as a disciplined extension of an “Information Audit” viewpoint within a locality-preserving quantum cellular automaton (QCA) framework. The central claim is scoped so it can be scrutinized: matter-like excitations are auditable images that are not certified at a single-site update, but only after an audit closes over a minimal local neighborhood. In three dimensions, a nearest-neighbor stencil suggests a (1+6) block of cardinality 7; under explicit circuit-locality and audit assumptions, we show a structural lower bound Daudit ≥ 7 on the micro-depth needed to incorporate all neighbor links into a joint certification. We then strengthen the theory beyond narrative plausibility by adding (i) an operational definition of copy time via Helstrom hypothesis testing, (ii) a quantum-speed-limit lower bound on τcopy via QFI/Bures geometry and a stiffness parameter χ, and—crucially for PRA standards—(iii) a minimal explicit translation-invariant QCA class (a 7-layer Floquet-QCA schedule) for which the small-momentum dispersion has an emergent effective mass meff derived from the circuit. In that class we prove a proposition: the certified-sector quasi-energy satisfies E(k) = p (veff∥¯hk∥)2 + (meffc2)2 +O(∥k∥2, θ2, ∥k∥θ), ith veff ∝ 1/Daudit and meffc2 ∝ √ χ/Daudit, both directly testable in QCA simulation. Finally, Planck→electroweak matching is kept as a discussion (not a result): it is presented only as a possible UV boundary-condition narrative, explicitly separated from the structural theorems.

•Jan 12, 2026•0 citations
We present a self-contained, audit-grade formulation of the Quantum Information Copy-Time (QICT) program as a micro–macro closure framework. The microscopic layer is strictly unitary and localitypreserving (a quantum cellular automaton, QCA), including a gauge-coded code-subspace construction and a continuum Dirac limit as a controlled long-wavelength approximation. The central micro–macro bottleneck is the emergence of diffusion from deterministic unitary dynamics. Rather than overclaiming a resolved theorem where the general problem remains open, we (i) replace informal “fast mixing” language by a structured, measurable spectral criterion in the hydrodynamic sector (SDC), and (ii) provide a quantitative bridge showing how certified second-moment (design-channel) diffusion controls infinite-temperature density correlators whenever a local approximate-design property holds (with explicit error bounds). We supply complementary numerical evidence: exact-unitary diagnostics by ED at L = 12 with an L = 14 cross-check, a max-L certification up to L = 512 at the momentchannel level, including a vanishing ballistic/Drude proxy, and a scalable unitary MPS–TEBD typicality diagnostic with explicit Drude bounds and bond-dimension convergence tests. We then propagate audited parameter intervals through a phenomenological closure map, with an explicit reproducibility contract (JSON, hashes, and PASS/FAIL verifier). All claims are labeled as PROVEN, CERTIFIEDNUMERICAL, EXTERNAL-DATUM, HYPOTHESIS, or CONJECTURE.
We present a maximal referee-grade formulation of the Quantum Information Copy Time (QICT) program. All claims are restricted to (i) standard Axioms (locality, stationarity/KMS, conservation), (ii) executable certification predicates, or (iii) Theorems with fully enumerated premises. The key observable is the copy time τcopy \tau_{\text{copy}} τcopy​, defined operationally via Helstrom distinguishability. A certified hydrodynamic-window predicate CHW (constructed from finite-time witnesses and residual tests) gates every micro--macro statement. Under CHW we derive diffusion and prove the central scaling τcopy=Θ ⁣(χmicro(2)) \tau_{\text{copy}} = \Theta\!\left(\sqrt{\chi^{(2)}_{\text{micro}}}\right) τcopy​=Θ(χmicro(2)​​), where χmicro(2)=⟨δQ, (−L⊥)−2 δQ⟩KM \chi^{(2)}_{\text{micro}}=\langle \delta Q,\,(-\mathcal{L}_\perp)^{-2}\,\delta Q\rangle_{\mathrm{KM}} χmicro(2)​=⟨δQ,(−L⊥​)−2δQ⟩KM​ is a second-moment fast-complement susceptibility. Optional bridges (thermal modular saturation and Higgs-portal matching) are isolated as explicit model Axioms; the "Golden Relation'' is then a Theorem and is non-circular provided an independent τcopy \tau_{\text{copy}} τcopy​ inference NC is satisfied. We include an explicit, dataset-level certification appendix (tables generated from bundled validation outputs), enabling direct audit.
We formulate and benchmark an operational timescale—the quantum information copy time—that quantifies how rapidly a localized bias in an initial many-body state becomes remotely certifiable using measurements restricted to a distant receiver region. The definition is intrinsically information-theoretic: for a fixed distinguishability threshold \eta \in (0,1), the copy time \tau_{\mathrm{copy}}(A \to B; \eta) is the earliest time at which the reduced states on B become distinguishable with advantage at least \eta, quantified by the trace distance and equivalently by the optimal Helstrom measurement. We present (i) a minimal theorem that isolates the genuinely nontrivial ingredients—locality, conservation laws, and an explicit receiver-observable class—and (ii) a controlled hydrodynamic closure in which the copy time is governed by a second-moment spectral susceptibility that ties the receiver advantage to the slowest transport mode. We then provide reproducible exact-diagonalization benchmarks in the XXZ chain that (a) extract finite-size transport diagnostics with conservative uncertainty quantification and (b) delineate failure modes in integrable and near-integrable regimes. TEBD/MPS calculations are included only as qualitative cross-checks (Supplementary File S1) and are not used to support asymptotic scaling claims. Finally, we include a brief, clearly separated outlook on how locality-preserving quantum cellular automata (QCA) and code-subspace constraints might shape operational copy-time distances; this material is explicitly conjectural and is not used in any theorem, bound, or numerical claim.
We formulate and benchmark an operational timescale—the quantum information copy time— that quantifies how fast a localized bias in an initial many-body state becomes remotely certifiable by measurements restricted to a distant receiver region. The definition is intrinsically information-theoretic: for a fixed distinguishability threshold η ∈ (0, 1), the copy time τcopy(A → B; η) is the earliest time at which the reduced states on B become distinguishable with advantage at least η, measured by trace distance and equivalently by the optimal Helstrom measurement. We present (i) a minimal theorem that isolates which inputs are genuinely nontrivial (locality, conservation laws, and an explicit receiver observable class), and (ii) a controlled hydrodynamic closure in which the copy time is governed by a second-moment spectral susceptibility that couples the receiver advantage to the slowest transport mode. We then provide reproducible exact-diagonalization benchmarks in the XXZ chain that (a) extract finite-size transport diagnostics with conservative uncertainty quantification and (b) delimit failure modes in integrable and near-integrable regimes. TEBD/MPS calculations are included only as qualitative cross-checks (Supplementary File S1) and are not used to support asymptotic scaling claims. Finally, we situate these results inside the broader QICT program, where locality-preserving quantum cellular automata (QCA) and code-subspace constraints motivate using copy-time distances as primitives for an operational geometry; we keep this outlook explicitly conjectural and separate from the proved/validated statements.
Abstract We formulate quantum-information copy time (QICT) as a conditional operator-algebraic criterion for diffusive infrared sectors of local quantum dynamical systems. The microscopic input is a physically accessible observable net rather than the full matrix algebra of all microscopic labels. This distinction is used throughout: locality, reversibility and exact charge conservation do not imply primitivity of the dynamical commutant once superselection or operationally inaccessible labels are present. We prove a fragmentation theorem on such observable nets, construct the Kubo-Mori fluctuation Hilbert space under exponential clustering, and state a closed QICT datum consisting of a primitive infrared centre, vanishing Drude projection, a sectorial Kubo-Mori Dirichlet form and absence of singular metric mass. The main theorem is a hydrodynamic Feshbach-Schur criterion: if the Bloch fibre of the effective generator is analytic at the origin and the QICT datum holds, then the isolated scalar copy mode has a diffusive pole with tensor λ(k) = −D ij k i k j + O(|k| 3 ), D ij = D ij bare + χ −1 ⟨Ji,M −1 J j ⟩ KM , M = −QL 0 Q. The criterion is non-empty: an exchange-dephasing quantum Markov sector verifies it on a closed one-density fluctuation sector, with an explicit observable net, stationary state, Bloch fibre, sectoriality and diffusion tensor. Gauge-code terminality and a scalar Higgs-portal benchmark enter only as applications under additional restricted hypotheses. The raw scalar benchmark is excluded by xenon direct-detection limits unless an independently derived copy-code form factor supplies the required suppression.
We develop an operational certification framework for micro–macro modeling in local quantum systems. Audited closure is defined as a uniform discrepancy bound between microscopic and surrogate predictions over a declared observable suite on a declared domain of states. A receiver-region copy time τ_copy(η;A→B) is defined as the earliest time at which a finite receiver region B can distinguish—at trace-distance threshold η—a localized perturbation supported on A. Under explicit Lieb–Robinson hypotheses for Hamiltonian or Lindbladian generators, we derive an exponential receiver distinguishability envelope and an explicit time-to-threshold lower bound, including the regime η≥Γ where the threshold is provably never reached and τ_copy=+∞. As an achieved-closure demonstration, we analyze a split-step quantum walk lifted to quasi-free lattice fermions and provide computable dispersion and two-point density audit bounds on a band-limited quasi-free domain. As a signature contribution beyond a repackaging of locality, we prove a locality–mixing separation theorem for primitive Lindbladians with a log-Sobolev (or mixing) rate λ: the receiver distinguishability is bounded by the minimum of a ballistic LR tail and an intrinsic mixing contraction, yielding a measurable crossover time and an operational separation between unitary and dissipative dynamics.
We formulate an operational hypothesis—the Synchronization Latency Principle—as a disciplined extension of an “Information Audit” viewpoint within a locality-preserving quantum cellular automaton (QCA) framework. The central claim is scoped so it can be scrutinized: matter-like excitations are auditable images that are not certified at a single-site update, but only after an audit closes over a minimal local neighborhood. In three dimensions, a nearest-neighbor stencil suggests a (1+6) block of cardinality 7; under explicit circuit-locality and audit assumptions, we show a structural lower bound Daudit ≥ 7 on the micro-depth needed to incorporate all neighbor links into a joint certification. We then strengthen the theory beyond narrative plausibility by adding (i) an operational definition of copy time via Helstrom hypothesis testing, (ii) a quantum-speed-limit lower bound on τcopy via QFI/Bures geometry and a stiffness parameter χ, and—crucially for PRA standards—(iii) a minimal explicit translation-invariant QCA class (a 7-layer Floquet-QCA schedule) for which the small-momentum dispersion has an emergent effective mass meff derived from the circuit. In that class we prove a proposition: the certified-sector quasi-energy satisfies E(k) = p (veff∥¯hk∥)2 + (meffc2)2 +O(∥k∥2, θ2, ∥k∥θ), ith veff ∝ 1/Daudit and meffc2 ∝ √ χ/Daudit, both directly testable in QCA simulation. Finally, Planck→electroweak matching is kept as a discussion (not a result): it is presented only as a possible UV boundary-condition narrative, explicitly separated from the structural theorems.