combine the two ideas: (i) using a star-topology molecule as an entangled magnetic sensor, and, (ii) engineering the noisy environment that surrounds the sensor considered.

Molecules as a Simulator of Entangled Magnetic Sensor {#TH_M_S}
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Assume an isolated nuclear spin of which initial state is $$\begin{aligned}
|\psi\rangle =  \frac{|0\rangle + | 1\rangle}{\sqrt{2}},\end{aligned}$$ where $|0\rangle$ and $|1\rangle$ are two eigenstates of the standard Pauli matrix $\sigma_z$. The system is exposed under a magnetic filed $B \vec{z}$ where $\vec{z}$ is the unit vector along the $z$-axis for a period of $\tau$, and becomes $$\begin{aligned}
|\psi_\tau\rangle =  \frac{|0\rangle + e^{i \gamma_{\rm G} B \tau}
| 1\rangle}{\sqrt{2}},\end{aligned}$$ where $\gamma_{\rm G}$ is the gyromagnetic ratio. Therefore, the acquired phase $\gamma_{\rm G} B \tau$ can be used to measure $B$. The sensitivity of a set of $N$ spins is proportional to $\sqrt{N}$: It is the SQL [@PhysRevLett.79.3865; @Giovannetti:2011aa].

Now, if we assume our sensor consists of $N$ spins with the initial state is entangled, such as $$\begin{aligned}
|\psi\rangle =  \frac{|00 \dots 0\rangle 
+ | 11 \dots 1\rangle}{\sqrt{2}},\end{aligned}$$ then, this state will evolve into $$\begin{aligned}
|\psi_\tau\rangle =  \frac{|00 \dots 0\rangle 
+ e^{i N \gamma_{\rm G} B \tau}| 11 
\dots 1\rangle}{\sqrt{2}},\end{aligned}$$ after a time $\tau$ and thus the 