Quantum Advantage in Private Multiple Hypothesis Testing

Abstract: For multiple hypothesis testing based on classical data samples, we demonstrate a quantum advantage in the optimal privacy-utility trade-off (PUT), where the privacy and utility measures are set to (quantum) local differential privacy and the pairwise-minimum Chernoff information, respectively. To show the quantum advantage, we consider some class of hypotheses that we coin smoothed point masses. For such hypotheses, we derive an upper bound of the optimal PUT achieved by classical mechanisms, which is tight for some cases, and propose a certain quantum mechanism which achieves a better PUT than the upper bound. The proposed quantum mechanism consists of a classical-quantum channel whose outputs are pure states corresponding to a symmetric informationally complete positive operator-valued measure (SIC-POVM), and a depolarizing channel.