Quantum Advantage for Two-Party Differential Privacy
A quantum protocol estimates two-party Hamming distance with constant information-theoretic differential-privacy error, beating classical square-root limits.
The paper gives information-theoretically private quantum protocols for two-party Hamming distance when both parties must output the same estimate. Classically, information-theoretic differential privacy requires about square-root-n error, while computational security can reach constant error. In Klauck's honest, nonpreemptive, message-preserving model, an O(n)-communication quantum protocol achieves pure epsilon quantum differential privacy with expected error at most 2/sinh(epsilon) plus any gamma greater than 0. Approximate (epsilon, delta) QDP yields still smaller error and keeps an O(1) versus Omega(square-root-n over log n) separation for delta = o(1/n). The authors separate this from weaker prescribed-channel privacy, which already has an exact classical realization, and from fully retention-robust security, where measurement-and-abort attacks remain possible.
- Classical information-theoretic DP needs about square-root-n error; computational security allows constant error.
- An O(n)-communication quantum protocol achieves pure epsilon quantum differential privacy.
- Expected error is at most 2/sinh(epsilon) plus any positive gamma.
- Approximate QDP preserves an O(1) versus roughly square-root-n over log-n separation.
- Preserving non-orthogonal quantum messages, not weaker channel privacy, enables the result.
From the original article
1 min read at arxiv.orgWe introduce information-theoretically private quantum protocols for two-party Hamming distance when both parties must output the same estimate. Classically, for input length $n$, information-theoretic protocols require $Ω(\sqrt{n})$ error under pure differential privacy and $Ω(\sqrt{n}/\log n)$ error under strong approximate differential privacy, whereas computational security permits $O(1)$ error.
By Daniel Alabi · arxiv.org
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