Certification Resources and the Value of Retained Quantum-Reader Records

This paper develops task-relative reader certification within Shadow Theory’s source–readout programme. It asks how many source copies are needed to validate a fixed quantum reader, and when access to its retained measurement records reduces that cost compared with observing only its final correct-or-incorrect decisions. The reader is fixed before validation and must return a sign after each complete experiment. A trusted evaluator knows the preparation label for scoring, while the reader does not. The analysis distinguishes terminal-error observations, records with trusted ancillary information, and readable measurement trajectories governed by a shared physical response model. For terminal-error validation, the paper establishes exact finite-budget tests and sequential likelihood tests, together with nearly matching information-theoretic lower bounds on expected source consumption. An unrestricted-record result shows why additional archived data alone need not improve certification: an advantage requires specified information or response constraints. A separate trusted-seed construction gives an exact information-projection test. The central quantitative comparison concerns a fixed fourteen-copy reader in a trusted shared-visibility family. To certify a maximum label error of one percent, a trajectory-based validator achieves a false-certificate probability of at most one in 1,048,576 and a nominal acceptance probability of at least 95 percent, using no more than 720,160 source copies. Under the same preparation and physical-response promises, every validator restricted to terminal errors and meeting the same acceptance requirement needs more than 1,992,371 source copies in expectation. At the exact nominal device, an uncapped trajectory-based test accepts almost surely with expected consumption below 254,746 copies. A separate robustness analysis extends likelihood-test validity to a quantified class of conditional response deviations. Finite-cap guarantees and expected stopping costs remain explicitly distinguished. The results demonstrate a certified resource advantage from access to retained classical measurement trajectories, rather than merely an improvement over one chosen terminal-error test. Supporting materials provide the fixed reader, exact certificates and reproducibility procedures. All guarantees depend on the stated preparation, response, information-access and deployment-stability assumptions. Certification concerns the nominated reader’s decision error; it does not establish complete quantum-instrument equivalence or identify an underlying source. The analysis uses standard quantum probabilities within Shadow Theory’s research programme.