Index privacy without assumption (P)

Prove index privacy for the one-way single-server QSPIR protocol against a server who departs from assumption (P), including servers that prepare states other than the prescribed BB84 states or falsely confirm which set guesses are correct.

Background

Assumption (P) requires that every photon emitted at a position carry the same prescribed BB84 state and that the server truthfully announce which set guesses were correct and which positions are retained. Under this assumption, the paper proves index privacy, with an additional multi-click bound for multiphoton signals.

The analysis explicitly excludes a server who tampers with the prepared states or falsely confirms set guesses. Such behavior can bias the client’s conclusive-position pattern across blocks and thereby correlate the announced set and shift with the requested index. The conclusion identifies extending index privacy to this adversarial setting as an open question.

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; Section~\ref{sec:Alice_cheating} and Appendix \ref{app:alice_audit}