A unifying framework for differentially private quantum algorithms

TL;DR

This paper introduces a comprehensive framework for quantum differential privacy, offering tighter guarantees and practical mechanisms for protecting sensitive quantum data, especially relevant for near-term quantum devices.

Contribution

It proposes a new general definition of neighboring quantum states, improving privacy guarantees and integrating classical and quantum noise for quantum measurements.

Findings

Exponential privacy guarantees for quantum measurements.

A new convexity property of quantum divergence proven.

Empirical estimation of robustness in quantum privacy mechanisms.

Abstract

Differential privacy is a widely used notion of security that enables the processing of sensitive information. In short, differentially private algorithms map "neighbouring" inputs to close output distributions. Prior work proposed several quantum extensions of differential privacy, each of them built on substantially different notions of neighbouring quantum states. In this paper, we propose a novel and general definition of neighbouring quantum states. We demonstrate that this definition captures the underlying structure of quantum encodings and can be used to provide exponentially tighter privacy guarantees for quantum measurements. Our approach combines the addition of classical and quantum noise and is motivated by the noisy nature of near-term quantum devices. Moreover, we also investigate an alternative setting where we are provided with multiple copies of the input state. In this case, differential privacy can be ensured with little loss in accuracy combining concentration of measure and noise-adding mechanisms. En route, we prove the advanced joint convexity of the quantum hockey-stick divergence and we demonstrate how this result can be applied to quantum differential privacy. Finally, we complement our theoretical findings with an empirical estimation of the certified adversarial robustness ensured by differentially private measurements.