Perturbation Analysis of Maximal Quantum Leakage

As quantum technologies integrate into communication and computing, protecting sensitive classical data encoded into quantum states is critical. Maximal Quantum Leakage (MQL) serves as a worst-case measure of an adversary's inference advantage when performing arbitrary quantum measurements. This paper investigates the robustness of MQL, specifically asking how much the leakage changes when the intended quantum encoding is subject to noise, hardware imperfections, or unintended interactions.

The authors analyze the sensitivity of MQL by comparing an ideal ensemble of quantum states to a perturbed version. They derive a Lipschitz-type continuity bound using the trace distance between the ideal and perturbed density operators. To provide practical utility, they also derive sufficient conditions for bounding MQL variation using fidelity and quantum relative entropy. The authors validate the tightness of the trace-distance bound by constructing a specific worst-case example and use numerical simulations to evaluate the looseness of the fidelity and relative-entropy-based bounds.

The study proves that the variation in MQL is bounded by the trace distance between the ideal and perturbed states, scaled by the minimum of the alphabet size and the Hilbert space dimension. This bound is shown to be tight, as there exist configurations where the leakage change reaches this limit. Furthermore, while the authors provide analytical bounds for fidelity and relative-entropy perturbations, numerical experiments reveal that these bounds are often loose, suggesting that they provide conservative estimates rather than tight characterizations of leakage sensitivity in realistic scenarios.