Quantum Advantage in Locally Differentially Private Hypothesis Testing

TL;DR

This paper demonstrates a quantum advantage in private hypothesis testing by proposing a quantum privacy mechanism that outperforms classical bounds in certain distribution scenarios, enhancing privacy-utility trade-offs.

Contribution

It introduces a quantum privacy mechanism that surpasses classical limits in privacy-utility trade-offs for hypothesis testing, especially with specific distributions.

Findings

Quantum mechanism achieves better privacy-utility trade-offs than classical bounds.

Quantum advantage demonstrated for smoothed point mass and uniform distributions.

Proposed quantum mechanism uses SIC states and depolarizing channel.

Abstract

We consider a private hypothesis testing scenario, including both symmetric and asymmetric testing, based on classical data samples. The utility is measured by the error exponents, namely the Chernoff information and the relative entropy, while privacy is measured in terms of classical or quantum local differential privacy. In this scenario, we show a quantum advantage with respect to the optimal privacy-utility trade-off (PUT) in certain cases. Specifically, we focus on distributions referred to as smoothed point mass distributions, along with the uniform distribution, as hypotheses. We then derive upper bounds on the optimal PUTs achievable by classical privacy mechanisms, which are tight in specific instances. To show the quantum advantage, we propose a particular quantum privacy mechanism that achieves better PUTs than these upper bounds in both symmetric and asymmetric testing. The proposed mechanism consists of a classical-quantum channel that prepares symmetric, informationally complete (SIC) states, followed by a depolarizing channel.