as in Fig. 2, Fig. 3 depicts $\overline{D} \equiv \frac{1}{2T}\int_{0}^{T}  ||\rho(t)-\rho_i|| dt $, i.e., the time-averaged distance between the actual time-evolving density matrix from that of a completely locked Bell state, for $c=T/100$ and $c=T/1000$, with different number of UDD pulses. It is seen that, at least for the number of UDD pulses considered here, $c=T/100=1/1000$ (about one hundredth of the decoherence time scale) already suffices to preserve a Bell state. That is, there seems to be no need to use much shorter pulses such as $c=T/1000=1/10000$, because the case of $c=T/1000$ (dashed line) in Fig. 3 shows little improvement as compared with the case of $c=T/100$ (solid line). This should be of practical interest for experimental studies of two-qubit decoherence suppression.

Finally, we show in Fig. 4 the decoherence suppression of a three-level quantum system, with the control operator given by Eq. (\[control3\]). Here the bath is modeled by other four three-level subsystems, and the total Hamiltonian is chosen as $$\begin{aligned}
 H & = & \sum_{m=2}^{5}\sum_{\alpha=\{x,y,z\}}b_{j,m}j_{\alpha, m}\nonumber \\
 &  & + \sum_{n=1}^{5}\sum_{\alpha=\{x,y,z\}}\sum_{m>n}^{5}\sum_{\beta=\{x,y,z\}}c_{\alpha\beta}j_{\alpha,m}j_{\beta,n}\nonumber \\
 &  & +\ H_{c},\end{aligned}$$ where $j_{\alpha,m}$ represents the $j_{x}$, $j_y$, or $j_z$ operator associated with the $m$th three-level subsystem, with the first being the central system 