Quantum differential privacy under noise channels

Quantum differential privacy is a way to protect privacy in quantum computing. It perturbs the final state of quantum computing by a specific quantum noise channel and makes the output useless to the attackers, so as to achieve privacy protection. In this paper, we study the quantum differential privacy under three channels: bit flip channel, phase flip channel and depolarizing channel. We calculate the privacy parameters for these three channels based on the proportional distance. We show the privacy protection capability by calculating the decay rates of the trace distances of two arbitrary quantum states before and after passing through the channels. Under the same privacy budget, we compare the fidelities, the trace distances between the real outputs and the outputs after entering the channels, and analyze the privacy protection performance of different quantum channels in detail.