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 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 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 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.
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.
This manuscript is submitted as a Hypothesis rather than as an announcement of a con- firmed physical theory. It defines Quantum Information Copy Time (QICT) as a receiver- limited certification time for transferred quantum or hydrodynamic information and consol- idates the resulting test statements into a de-duplicated supplementary prediction ledger. The scientific purpose is restricted: to specify assumptions, falsification routes, and ob- servational or laboratory discriminants, not to claim discovery of dark matter, dark en- ergy, emergent gravity, or early-galaxy anomalies. After duplicate removal, cosmic-dawn integration, and the latest author-supplied cosmology update, the ledger still contains 99 non-redundant conditional statements. The strongest claims concern operational trans- port, locality constraints, open-system spectral criteria, and explicit failure conditions; the particle-physics, cosmological, gravitational, and cosmic-dawn entries are retained only as conditional benchmark tests requiring independent computation or data confrontation. All numerical windows are therefore presented as model-dependent targets. The manuscript includes data-availability, conflict-of-interest, funding, ethics, and AI-assisted-preparation statements to comply with preprint screening requirements.
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 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, 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)), where 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 inference NC is satisfied. We include an explicit, dataset-level certification appendix (tables generated from bundled validation outputs), enabling direct audit.