Adversarial Stress Tests for Quantum Certification

TL;DR

This paper introduces a framework for quantum certification that accounts for operational deviations, using a robustness gap to distinguish genuine quantum behavior from classical misalignments in realistic settings.

Contribution

It formalizes a protocol-agnostic diagnostic method based on a martingale-safe confidence bound to identify misalignments and false certifications in semi-device-independent quantum tests.

Findings

The robustness gap effectively separates statistical fluctuations from structural errors.

Postselection can inflate scores, but unconditional scoring maintains operational meaning.

Adaptive classical agents do not expand the classical set but recover the effective classical ceiling.

Abstract

We develop a practical framework for semi-device-independent (SDI) certification under operational deviations from the ideal protocol model. Apparent violations of classical benchmarks need not signal genuinely non-classical behaviour; they can arise from misalignment between (i) the scoring rule, (ii) the finite-sample statistical bound applied to that score, and (iii) the operational model realised in the experiment, including bias, memory, drift, and selection effects. We formalise a protocol-agnostic alignment principle based on a martingale-safe lower confidence bound and an operationally consistent effective classical ceiling. This yields a quantitative diagnostic, the \emph{robustness gap} $\Delta_{\mathrm{rob}} = S_{\mathrm{low}} - S_{C,\mathrm{eff}}$, which separates statistical fluctuations from structural modelling errors. Statistical deviations vanish asymptotically, whereas model misalignment can produce persistent false certification unless the benchmark is corrected. Using the $2\!\to\!1$ random access code as a minimal SDI testbed, we show that postselection can inflate conditional scores, whereas unconditional scoring restores the correct operational meaning of the witness. We further show that adaptive learning-based classical agents do not enlarge the admissible classical set; rather, they recover the effective classical ceiling implied by the operational model. The resulting framework provides a systematic diagnostic for certification in realistic quantum communication and measurement settings with embedded classical control, adaptive processing, and nonideal data acquisition.