Approximate-privacy improvement for retention-robust protocols

Determine whether approximate varepsilon,delta-retention-robust quantum differential privacy permits an accuracy improvement over the pure-privacy randomized-response baseline for common-output Hamming distance.

Background

The paper gives a retention-robust protocol based on randomized response for Alice’s input and geometric output noise for Bob’s input. The protocol satisfies pure quantum differential privacy against arbitrary retention-capable completely positive trace-preserving strategies, but its error is of order sqrt n for constant privacy parameters.

The table states that the same pure-private protocol also satisfies approximate privacy, while explicitly identifying as unresolved whether using a positive delta budget can yield a sharper error guarantee in the retention-robust model. This is distinct from the paper’s solved approximate-privacy calibration in the weaker KHNP model.