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We study the problem of robust performance of quantum systems understructured uncertainties. A specific feature of closed (Hamiltonian) quantumsystems is that their poles lie on the imaginary axis and that neither acoherent controller nor physically relevant structured uncertainties can alterthis situation. This changes for open systems where decoherence ensuresasymptotic stability and creates a unique landscape of pure performancerobustness, with the distinctive feature that closed-loop stability is securedby the underlying physics and needs not be enforced. This stability, however,is often detrimental to quantum-enhanced performance, and additiveperturbations of the Hamiltonian give rise to dynamic generators that arenonlinear in the perturbed parameters, invalidating classical paradigms toassess robustness to structured perturbations such as singular value analysis.This problem is addressed using a fixed-point iteration approach to determine amaximum perturbation strength $\delta_{\max}$ that ensures that the transferfunction remains bounded, $||T_\delta||<\delta^{-1}$ for$\delta<\delta_{\max}$.

Robustness of Quantum Systems Subject to Decoherence: Structured Singular Value Analysis?