Fig. 3: Visualization of query complexities for ε-perturbed unitary channels.
From: On the query complexity of unitary channel certification
The spherical shell represents the set of ε-perturbed unitary channels sampled from ε−CUE. The green region represents average-case channels, which can be certified using \({\mathcal{O}}(1/{\varepsilon }^{2})\) queries. The red region represents the single-basis rotation ensemble Eε, which requires \(\Omega (\sqrt{d}/\varepsilon )\) queries for certification. The white region represents a small exceptional subset of measure \(\exp (-\Omega (d))\) with unknown complexity. Note that the colored regions do not correspond to genuine geometric relations in the space of ε−CUE.
