Quantum advantage under fully retention-robust security

Determine whether quantum communication can improve the accuracy of two-party Hamming-distance computation under fully retention-robust security against arbitrary malicious or retention-capable quantum strategies.

Background

The paper establishes an information-theoretic quantum advantage for two-party Hamming distance only in Klauck’s honest, nonpreemptive, message-preserving model. In that model, an observing party must return the prescribed non-orthogonal quantum message, and equal-Gram rigidity prevents it from retaining input-dependent complementary information.

The stronger retention-robust model permits arbitrary quantum deviations, including measurement, message modification, retention, and abort. The authors exhibit a measure-and-abort attack that distinguishes adjacent inputs, so their guarded coherent protocol does not provide privacy in this stronger setting. The unresolved problem is whether some quantum protocol can nevertheless achieve improved accuracy while remaining secure against such fully retention-capable adversaries.