Differential Privacy of Quantum and Quantum-Inspired Classical Recommendation Algorithms

TL;DR

This paper demonstrates that quantum and quantum-inspired recommendation algorithms inherently provide differential privacy through their measurement randomness, eliminating the need for additional noise, with theoretical guarantees and empirical validation.

Contribution

It shows that the inherent randomness in quantum recommendation algorithms can ensure differential privacy without extra noise, providing theoretical bounds and empirical validation.

Findings

Achieves $( ext{ε,δ})$-DP with bounds depending on system parameters.

In typical regimes, privacy parameters scale as $ ilde{O}(1/\sqrt{n})$ and $ ilde{O}(1/\min^2\{m,n\})$.

Empirical results validate the privacy scaling on real datasets.

Abstract

We study the differential privacy (DP) of the quantum recommendation algorithm of Kerenidis--Prakash and its quantum-inspired classical counterpart. Under standard low-rank and incoherence assumptions on the preference matrix, we show that the randomness already present in the algorithms' measurement/$\ell_2$-sampling steps can act as a privacy-curating mechanism, yielding $(\varepsilon,\delta)$-DP without injecting additional DP noise through the interface. Concretely, for a system with $m$ users and $n$ items and rank parameter $k$, we prove $\varepsilon=\mathcal O(\sqrt{k/n})$ and $\delta= \mathcal O\big(k^2/\min^2\{m,n\}\big)$; in the typical regime $k=\mathrm{polylog}(m,n)$ this simplifies to $\varepsilon=\tilde{\mathcal O}(1/\sqrt n)$ and $\delta=\tilde{\mathcal O}\big(1/\min^2\{m,n\}\big)$. Our analysis introduces a perturbation technique for truncated SVD under a single-entry update, which tracks the induced change in the low-rank reconstruction while avoiding unstable singular-vector comparisons. Finally, we validate the scaling on real-world rating datasets and compare against classical DP recommender baselines.