Maximal Information Leakage from Quantum Encoding of Classical Data

A new measure of information leakage for quantum encoding of classical data is defined. An adversary can access a single copy of the state of a quantum system that encodes some classical data and is interested in correctly guessing a general randomized or deterministic function of the data (e.g., a specific feature or attribute of the data in quantum machine learning) that is unknown to the security analyst. The resulting measure of information leakage, referred to as maximal quantum leakage, is the multiplicative increase of the probability of correctly guessing any function of the classical data upon observing measurements of the quantum state. Maximal quantum leakage is shown to satisfy post-processing inequality (i.e., applying a quantum channel reduces information leakage) and independence property (i.e., leakage is zero if the quantum state is independent of the classical data), which are fundamental properties required for privacy and security analysis. It also bounds accessible information. Effects of global and local depolarizing noise models on the maximal quantum leakage are established.