& 1\\
1 &  & 1\\
 & 1\end{array}\right), \nonumber \\
 j_{y}&=&\frac{1}{\sqrt{2}}\left(\begin{array}{ccc}
 & -i\\
i &  & -i\\
 & i\end{array}\right), \nonumber \\
   j_{z}& =&\left(\begin{array}{ccc}
1\\
 & 0\\
 &  & -1\end{array}\right).\end{aligned}$$ As an example, we use the state $(1,0,0)^{\text{T}}$ to define our coherence measure. The associated control operator $V_1$ is then found to be $$\begin{aligned}
\label{control3}
V_1=j_{z}+j_{z}^{2}-I.\end{aligned}$$ Interestingly, this control operator involves a nonlinear function of the angular momentum operator $j_z$. This requirement can be experimentally fulfilled, because realizing such kind of operators in a pulsed fashion is one main achievement of Ref. [@Jessen], where a “kicked-top" system is realized for the first time. The two different contexts, i.e., UDD by instantaneous pulses and the delta-kicked top model for understanding quantum-classical correspondence and quantum chaos [@Jessen; @haake; @Gongprl], can thus be connected to each other.

For the sake of completeness, we also present below those operators that commute with $V_1$, namely, $$\begin{aligned}
V_{2} & = &I+\frac{1}{2}j_{z}-\frac{1}{2}j_{z}^{2}, \nonumber\\
V_{3} & =& -I-\frac{1}{2}j_{z}+\frac{5}{2}j_{z}^{2}, \nonumber\\
V_{4} & =& -\frac{1}{\sqrt{2}}(j_{+}j_{z}+j_{z}j_{-}), \nonumber \\
V_5 & =& \frac{i}{\sqrt{2}}(j_{+}j_{z}-j_{z}j_{-}),\end{aligned}$$ where $j_{\pm}=j_{x}\pm ij_{y}$; and those operators that anti-commute with $V_1$, namely, $$\begin{aligned}
V_{6} & =& \frac{1}{\sqrt{2}}(j_{z}j_{+}+j_{-}j_{z}), \nonumber \\
V_{7} & =&\frac{i}{\sqrt{2}}(j_{-}j_{z}-j_{z}j_{+}),\nonumber \\
V_{8} & =&\frac{1}{2}(j_{+}^{2}+j_{-}^{2}), \nonumber \\
V_{9} & =& 