Speaker
Description
Differential privacy is the de-facto standard for privacy-preserving data analysis, and recently it has been extended to the quantum realm. We study how to answer counting queries on quantum-encoded datasets while preserving privacy. A counting query asks for the fraction of records satisfying a Boolean predicate, such as 'How many people in the dataset are students and within the age bracket 25–34?'. Counting queries form the most basic but nonetheless rich set of statistics extractable from a dataset. We show that answering these queries on a quantum encoded dataset reduces to measuring the amplitude of one of two orthogonal subspaces: a “good” subspace containing records satisfying the predicate and a “bad” subspace containing the rest. Hence the query answer is exactly the probability of the good component. This observation reduces differentially private counting-query release to private amplitude estimation. We analyse two mechanisms. First, for repeated computational-basis measurements, we prove refined $(\epsilon, \delta)$-differential privacy guarantees that exploit the sampling randomness induced by measurement. This yields privacy amplification and requires less explicit Laplace noise than generic quantum differential privacy bounds for arbitrary measurements. Second, for canonical quantum amplitude estimation, which estimates the query answer using $\mathcal{O}(1/\Delta)$ coherent queries rather than the $\mathcal{O}(1/\Delta^2)$ samples required by direct measurement, we derive a tight global sensitivity bound for the phase variable, namely $\sin^{-1}(1/\sqrt{n})$, and use it to construct a modified $(\epsilon, 0)$-differentially private amplitude-estimation protocol that achieves privacy by injecting calibrated Laplace noise directly into the phase eigenvalue. We also discuss delegated evaluation using the quantum one-time pad and how inherent depolarizing noise can contribute to the overall privacy budget.
Full paper: Answering Counting Queries with Differential Privacy on a Quantum Computer
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