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