Figure 2. The distribution of the $\mathrm{log}$ scaling ratio between the minimum variances of ω in the coherent state and Fock state. We set ${\mu }^{-2}$ as the unit of the frequencies and let the total energy levels, i.e. ${n}_{1}+{n}_{2}$ or $| {\alpha }_{1}{| }^{2}+| {\alpha }_{2}{| }^{2}$ is 100. κ represents the evolutionary time. Points with value larger than zero means fork state is better, otherwise the coherent state case gets more precise measurement result.
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