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 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 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.
We introduce an operational notion of transport latency, which we call quantum information copy time: the earliest time at which a receiver confined to a region B can certify, with prescribed advantage, which of two global hypotheses was prepared by local operations in a distant sender region A. The benchmark object is information-theoretic—the Helstrom advantage on B, given by the trace distance between reduced states—and it also admits receiver-restricted refinements that make measurement constraints explicit, including few-body and moment-channel receivers. We derive the corresponding kinematic locality constraints for Hamiltonian and Lindbladian dynamics with Lieb–Robinson tails, as well as for circuits and quantum cellular automata with strict light cones. We then establish a diffusive benchmark in the quantum symmetric simple exclusion process (Q-SSEP): for locally prepared charge-biased hypotheses, the Helstrom copy time obeys an unconditional diffusion-limited lower bound expressed in terms of the diffusion constant D and the static susceptibility χ. For closed Hamiltonian systems, we formulate a projection-based route—with assumptions stated explicitly—that relates restricted copy times to a single slow transport pole on a diagnostically checkable time window. We complement the analytical framework with conservative exact-diagonalization diagnostics in the XXZ chain and with a bundled TEBD/MPS reference implementation plus convergence protocol (Supplementary S2 and Code SC1), validated against exact evolution at small sizes. Finally, we compare copy time with scrambling diagnostics based on out-of-time-ordered correlators and identify regimes in which conservation laws delay certifiability well beyond the ballistic operator-growth front.
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 introduce quantum information copy time as a task-defined latency for transport: it is theearliest time at which a receiver confined to a region B can certify, with prescribed advantage,which of two global hypotheses was prepared by local operations in a distant sender region A.The benchmark definition is information-theoretic—the Helstrom advantage on B, given bythe trace distance between reduced states—and it admits natural refinements that incorporateexplicit measurement restrictions (few-body and moment channels). We first derive kinematiclocality constraints for Hamiltonian/Lindbladian dynamics with Lieb–Robinson tails and forcircuits/quantum cellular automata with strict light cones. We then establish a theorem-leveldiffusive benchmark in the quantum symmetric simple exclusion process (Q-SSEP): for locallyprepared charge-biased hypotheses, the Helstrom copy time obeys an unconditional diffusion-limited lower bound expressed in terms of the diffusion constant Dand the static susceptibility χ.For closed Hamiltonian systems we formulate, with assumptions stated explicitly, a projection-based route that ties restricted copy times to a single slow transport pole on a diagnosticallycheckable time window. We provide conservative exact-diagonalization diagnostics in the XXZchain together with a bundled TEBD/MPS reference implementation and convergence protocol(Supplementary S2 and Code SC1), validated against exact evolution on small sizes; large-LTEBD studies are left as future work. Finally, we contrast copy time with scrambling diagnosticsbased on out-of-time-ordered correlators and identify regimes in which conservation laws delaycertifiability well beyond the ballistic operator-growth front.
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.