time-inhomogeneous noisy environments of the side spins (two $\circ$’s) as we discussed in Refs. [@kondo2016; @Iwakura2017; @Kondo2018; @kondo2007; @PhysRevA.55.2290; @PhysRevLett.120.030402]. Note that we assume here that only the nearest neighbor interactions are important. After all, we can engineer the environment of the sensor ($\circ-\bigcirc-\circ$).

Experiments
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In this section, we describe our approach to simulate an entangled sensor under an engineered environment with a molecule solved in an isotropic liquid. First, we show how to prepare an engineered Markovian environment and then discuss how to simulate an entangled sensor under an engineered time-inhomogeneous noisy environment.

Engineered Markovian Environment
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Solute molecules in an isotropic liquid are rapidly moving and also influenced by an strong external magnetic field. Thus, the interactions among nuclear spins in the solute and solvent molecules are averaged out [@Levitt2008]. In other words, the solute molecules are approximated to be isolated, or there is no influence from the solvent (the environment).

To engineer a Markovian environment, magnetic impurities, such as Fe(III), are added into the solution. Since the magnetic impurity moves rapidly and randomly, it works as a Markovian environment and flip-flops the solute molecules’ nuclear spins randomly. The flip-flopping rate is proportional to the concentration of 