Windowed Finite-Size Scaling of Reference-State Information Backflow in Disordered Quantum Reservoirs

This record contains the v16 baseline dataset, analysis outputs, and manuscript draft for a finite-size scaling study of reference-state information backflow in disordered quantum reservoirs. The study investigates a two-qubit subsystem coupled to a finite disordered XY spin-chain reservoir with reservoir-local leakage. For each reservoir size, disorder strength, leakage strength, and random disorder seed, the composite system is evolved and the reduced subsystem state is compared to a fixed Bell-state reference using trace distance. The positive time derivative of this trace distance defines a reference-state information-backflow diagnostic. The completed v16 ensemble contains 34,560 simulation records spanning reservoir sizes N = 2–6, eighteen disorder values in omega ∈ [0.34, 0.48], six leakage strengths gamma_res = {0, 0.01, 0.02, 0.04, 0.07, 0.10}, and sixty-four random disorder seeds per parameter point. The leakage-dependent suppression of the diagnostic is fit to N_ref(gamma_res) = A exp(-k gamma_res) + C, where k defines an emergent Markovianization rate. The analysis introduces a windowed finite-size scaling relation, k(N, omega) ~ N^{alpha_w(omega)}, to distinguish boundary-dominated minimal reservoirs from extended-reservoir scaling behavior. The primary transition analysis identifies a crossover near omega_c ≈ 0.417, while the N ≥ 3 windowed analysis identifies a closely related crossover near omega_c ≈ 0.411. The deeper N ≥ 4 window remains memory-preserving across the sampled interval but trends upward with increasing disorder. This release is intended as a reproducible baseline dataset for studying finite-size effects, reference-state information backflow, and emergent Markovianization in structured open quantum systems. An N = 7 extension under the same protocol is in progress and may be deposited as a later version.