  In this paper, we examine the role of stochastic quantizers for privacy
preservation. We first employ a static stochastic quantizer and investigate its
corresponding privacy-preserving properties. Specifically, we demonstrate that
a sufficiently large quantization step guarantees $(0, \delta)$ differential
privacy. Additionally, the degradation of control performance caused by
quantization is evaluated as the tracking error of output regulation. These two
analyses characterize the trade-off between privacy and control performance,
determined by the quantization step. This insight enables us to use
quantization intentionally as a means to achieve the seemingly conflicting two
goals of maintaining control performance and preserving privacy at the same
time; towards this end, we further investigate a dynamic stochastic quantizer.
Under a stability assumption, the dynamic stochastic quantizer can enhance
privacy, more than the static one, while achieving the same control
performance. We further handle the unstable case by additionally applying input
Gaussian noise.
