Figure 4

Results for both noise channels, the over- and under-rotation (a)-(d) and the depolarizing channel (e)-(h) and for both interactions, the Heisenberg interaction (blue, red) and the Ising interaction (green, orange): We present the quality measure \(\mathcal{Q}_{\mathrm{MUB}}\) for the quorum formed by a complete set of MUBs with lowest possible entangling time (a), (e); the ratio of the quality measures for the numerically optimized quorum, \(\mathcal{Q}_{\mathrm{opt}}\) and \(\mathcal{Q}_{\mathrm{MUB}}\) (b), (f); as well as the normalized entangling times α (for Heisenberg interaction) (c), (d) and \(\tau ^{I}\) for the Ising interaction (g), (h). All these quantities are given as a function of the noise parameters r (a)-(d) and ζ (e)-(h). Note that the solid and dashed lines connecting the data points are guidance for the eyes while the dashed lines in (c), (d), (g), (h) represent the (smallest possible) normalized entangling time for the MUBs. The increase in \(\tau ^{I}\) from \(r=0.28\) to \(r=0.3\) might be due to the fact that \(\mathcal{Q}_{N}\) can be invariant under switching on the Ising-interaction for certain states, see main text