Noise-tolerant certificate for the client’s measurement

Establish a certificate for the client’s unambiguous-state-discrimination measurement that remains valid in the presence of channel noise, thereby extending the measurement certification beyond the noiseless-channel analysis.

Background

The protocol’s database-privacy proof relies on certifying that the client measures each received quantum system individually and achieves a known rate close to the prescribed unambiguous-discrimination rate. Appendix \ref{app:usd_certification} provides such a certificate only for the noiseless measurement-test table; the conclusion identifies tolerance to channel noise as unresolved.

A noise-tolerant certificate is needed because channel asymmetries can perturb the declaration frequencies and the inconclusive-outcome posterior, potentially invalidating the erasure-based privacy analysis or requiring additional slack in the certified known-rate.

References

Three questions remain open: a certificate of the client's measurement that tolerates channel noise, a cheaper joint permutation than the storage-model commitment of Step~\ref{QSPIR:shuffle}, and index privacy against a server who departs from assumption (P).

— One-Way Quantum Symmetric Private Information Retrieval Protocol From A Single Database Server Using NISQ Devices  (2610.02093 - Zou et al., 1 Oct 2026) in Conclusion, final paragraph