Operational Certification Horizons in Quantum Transport: Copy Time, Conservation Laws, and a Rigorous Diffusive Benchmark

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.