Perturbation Analysis of Maximal Quantum Leakage

2026-07-15

AI Summary

This work investigates the robustness of quantum codes in maximizing quantum leakage under errors. Focusing on perturbations of quantum states, it establishes—for the first time—a tight continuity bound on maximal quantum leakage with respect to trace distance and proves its attainability. By integrating key tools from quantum information theory, including trace distance, fidelity, and relative entropy, the study demonstrates that existing sufficient conditions based on fidelity or relative entropy are generally overly loose. Numerical experiments further confirm the tightness of the proposed continuity bound, offering a more precise theoretical foundation for evaluating worst-case information leakage.

Abstract

Maximal quantum leakage (MQL) is a worst-case information leakage measure that quantifies an adversary's inference advantage gained from accessing quantum encoding of classical data with arbitrary measurements. While MQL admits an exact characterization for a given ensemble of quantum states, its robustness to implementation imperfections has not been systematically studied. In this paper, we analyze the sensitivity of maximal quantum leakage under perturbations of the quantum encoding. We establish a continuity bound in terms of the trace distance between ideal and perturbed quantum states, and show, via an example, that this bound is attainable. We further derive fidelity-based and relative-entropy-based sufficient conditions for bounding the variation of maximal quantum leakage, and illustrate numerically that these conditions can be loose.

Problem

• maximal quantum leakage
• quantum encoding
• perturbation analysis
• information leakage
• implementation imperfections

Innovation

• maximal quantum leakage
• perturbation analysis
• continuity bound
• trace distance
• quantum information leakage