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

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.