\Psi|-I,\end{aligned}$$ where $I$ is the identity operator. This polarization operator has the following properties: $$\begin{aligned}
\label{Y1property}
{\cal P}_{|\Psi\rangle}^2&=&I, \nonumber \\
{\cal P}_{|\Psi\rangle}|\Psi\rangle&=&|\Psi\rangle, \nonumber \\
{\cal P}_{|\Psi\rangle}|\Psi^{\perp}\rangle &=& -|\Psi^{\perp}\rangle,\end{aligned}$$ where $|\Psi^{\perp}\rangle$ represents all other possible states of the system that are orthogonal to $|\Psi\rangle$. Hence, if the expectation value of ${\cal P}_{|\Psi\rangle}$ is unity, then the system must be on the state $|\Psi\rangle$. In this sense, the expectation value of ${\cal P}_{|\Psi\rangle}$ measures how much coherence of the $|\Psi\rangle$-type is contained in a given system. For example, in the single-qubit case, ${\cal P}_{|\Psi\rangle}$ measures the longitudinal coherence if $|\Psi\rangle$ is chosen as the spin-up state, but measures the transverse coherence along a certain direction if $|\Psi\rangle$ is chosen as a superposition of spin-up and spin-down states. Most important of all, as seen in the following, the generalized polarization operator ${\cal P}_{|\Psi\rangle}$ can directly give the required control Hamiltonian in order to preserve the quantum coherence thus defined.

We now consider a two-qubit system interacting with an arbitrary bath whose self-Hamiltonian is given by $H_{E}=c_0$. The qubits interact with the environment via the interaction Hamiltonian $H_{jE}=\sigma_{x}^{j}c_{x,j}+\sigma_{y}^{j}c_{y,j}+\sigma_{z}^{j}c_{z,j}$ for $j=1,2$, where $\sigma_x^{j}$, $\sigma_{y}^{j}$, and $\sigma_z^{j}$ are the standard Pauli matrices, and $c_{\alpha,j}$ are bath 