Persistence of the coherent advantage under repeated message use

Determine whether the quantum-reference advantage persists when the leakage-detection procedure is used repeatedly and anomalous messages disturb the references, create correlations, and permit classical calibration costs to be amortized over multiple messages.

Background

The main results concern a single message with independent quantum references and no prior calibration. Under those conditions, coherent reference processing has a dimension-independent budget for a fixed detection target, whereas measurement-first processing requires a budget that scales with the ambient dimension.

The paper leaves unresolved whether this separation survives repeated use. Repeated operation can invalidate the independence assumptions because anomalous messages may disturb the references and correlate with them; at the same time, the cost of classical calibration could be amortized across multiple messages.

References

Repeated use raises a complementary question: whether the advantage survives as anomalous messages disturb the references and create correlations, and as classical calibration costs are amortized over multiple messages.

— Exponential Advantage of Quantum over Classical References in Leakage Detection  (2609.36541 - An, 29 Sep 2026) in Discussion section