Classical Mechanism is Optimal in Classical-Quantum Differentially Private Mechanisms

Differential privacy (DP) is an influential privacy measure and has been studied to protect private data. DP has been often studied in classical probability theory, but few researchers studied quantum versions of DP. In this paper, we consider classical-quantum DP mechanisms which (i) convert binary private data to quantum states and (ii) satisfy a quantum version of the DP constraint. The class of classical-quantum DP mechanisms contains classical DP mechanisms. As a main result, we show that some classical DP mechanism optimizes any information quantity satisfying the information processing inequality. Therefore, the performance of classical DP mechanisms attains that of classical-quantum DP mechanisms.