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.
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.
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 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 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.
We present a self-contained, publication-oriented formulation of Quantum Information CopyTime (QICT), a timescale governing the certifiable replication of a conserved information labelY in local quantum many-body systems. The framework is built from an inverse-Liouvillianquadratic form in the Kubo–Mori (Bogoliubov) operator Hilbert space. To make the constructionmathematically well-posed and operational, we (i) define QICT using the Moore–Penrose pseu-doinverse of the Liouvillian generator (no hydrodynamic closure assumed), (ii) derive an exactspectral representation with a sharp finiteness criterion, (iii) introduce a controlled infrared (IR)regularization tcopy(Y; ϵ), and (iv) specify an explicit local certification task: binary hypothesistesting between opposite small biases ±θ in a local Gibbs family using filtered local currents.We prove that the exponential filter Jϵ =∞0 e−ϵt˙Y(t) dt is canonical in two precise senses: it is(a) the unique readout of a minimal Markovian “detector with finite memory” and (b) the resol-vent/Laplace transform naturally produced by linear response. We then link the signal-to-noiseratio (SNR) of any such certification protocol to the regulated QICT functional and providea hypothesis-testing translation from SNR to target error probability δ via standard inequali-ties. Finally, we state a transport-regime agnostic “Master” Golden Relation (free dynamicalexponent z), provide benchmark estimates for the matching constant CΛ using independentlycomputed chaos/transport inputs in canonical strong- and weak-coupling limits, and propagatetemperature-dependent transport uncertainties into the resulting mass band.
We introduce an operational transport latency, quantum information copy time: the earliesttime at which a receiver confined to a region B can certify, with prescribed advantage, whichof two global hypotheses was prepared by local operations in a distant sender region A. The benchmark quantity is information-theoretic—the Helstrom advantage on B, namely the tracedistance between the reduced states—and it also admits receiver-restricted refinements that makemeasurement constraints explicit, including few-body and moment-channel receivers. We derivethe corresponding kinematic locality constraints for Hamiltonian and Lindbladian dynamicswith Lieb–Robinson tails, as well as for circuits and quantum cellular automata with strictlight cones. We then establish the theorem-level anchor of the manuscript in the quantumsymmetric simple exclusion process (Q-SSEP): for locally prepared charge-biased hypotheses,the Helstrom copy time obeys an unconditional diffusion-limited lower bound expressed in termsof the diffusion constant D and the static susceptibility χ. For closed Hamiltonian systems,we formulate a projection-based reduction in which the operational scaling statement is made conditional on explicit, diagnostically checkable hypotheses, thereby separating what is provedmicroscopically from what is inferred in a controlled hydrodynamic window. We complement the analytical framework with exact-diagonalization diagnostics in the XXZ chain and with abundled TEBD/MPS reference protocol plus validation suite (Supplementary S2 and Code SC1),explicitly cross-validated against exact evolution at small sizes. In the strengthened submissionwe add three robustness layers beyond the original ED figures: an eight-size common-windowtransport sweep for the nonintegrable XXZ structure-factor diagnostic, an extractor-robustness check comparing first-crossing and sustained-crossing copy-time rules on the same Helstrom dataset, and a receiver-side validation dataset showing when a simple block-charge measurement saturates the Helstrom advantage in a controlled conserving reference model. Finally, we comparecopy time with scrambling diagnostics based on out-of-time-ordered correlators and show how conservation laws can delay certifiability well beyond the ballistic operator-growth front without any contradiction with locality.
We introduce an operational transport latency, quantum information copy time: the earliesttime at which a receiver confined to a region B can certify, with prescribed advantage, whichof two global hypotheses was prepared by local operations in a distant sender region A. The benchmark quantity is information-theoretic—the Helstrom advantage on B, namely the tracedistance between the reduced states—and it also admits receiver-restricted refinements that makemeasurement constraints explicit, including few-body and moment-channel receivers. We derivethe corresponding kinematic locality constraints for Hamiltonian and Lindbladian dynamicswith Lieb–Robinson tails, as well as for circuits and quantum cellular automata with strictlight cones. We then establish the theorem-level anchor of the manuscript in the quantumsymmetric simple exclusion process (Q-SSEP): for locally prepared charge-biased hypotheses,the Helstrom copy time obeys an unconditional diffusion-limited lower bound expressed in termsof the diffusion constant D and the static susceptibility χ. For closed Hamiltonian systems,we formulate a projection-based reduction in which the operational scaling statement is made conditional on explicit, diagnostically checkable hypotheses, thereby separating what is provedmicroscopically from what is inferred in a controlled hydrodynamic window. We complement the analytical framework with exact-diagonalization diagnostics in the XXZ chain and with abundled TEBD/MPS reference protocol plus validation suite (Supplementary S2 and Code SC1),explicitly cross-validated against exact evolution at small sizes. In the strengthened submissionwe add three robustness layers beyond the original ED figures: an eight-size common-windowtransport sweep for the nonintegrable XXZ structure-factor diagnostic, an extractor-robustness check comparing first-crossing and sustained-crossing copy-time rules on the same Helstrom dataset, and a receiver-side validation dataset showing when a simple block-charge measurement saturates the Helstrom advantage in a controlled conserving reference model. Finally, we comparecopy time with scrambling diagnostics based on out-of-time-ordered correlators and show how conservation laws can delay certifiability well beyond the ballistic operator-growth front without any contradiction with locality.