Maximal Information Leakage from Quantum Encoding of Classical Data

TL;DR

This paper introduces a new measure called maximal quantum leakage to quantify information leakage in quantum encoding of classical data, with properties suitable for privacy analysis and effects under noise models.

Contribution

It defines maximal quantum leakage, proves its key properties, and analyzes its behavior under noise, advancing quantum privacy measurement methods.

Findings

Maximal quantum leakage satisfies post-processing inequality.

It is zero when quantum states are independent of data.

Noise models affect the leakage bounds.

Abstract

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.