weak value amplification (II): when the detector cannot differentiate between two signals {#advantages-of-using-weak-value-amplification-ii-when-the-detector-cannot-differentiate-between-two-signals .unnumbered}
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As second example, let us consider that specific experimental conditions makes hard, even impossible, to detect very similar modes, i.e., with mode overlap $\rho \sim 1$. We can represent this by assuming that there is an [*effective*]{} mode overlap ($\rho_{\mathrm{eff}}$) which takes into account all relevant experimental limitations of a specific set-up, given by $$\rho \Longrightarrow \rho_{\mathrm{eff}}=1-(1-\rho)\exp \left[
-\left(\frac{\rho}{a}\right)^n \right].$$ Fig. 5 shows an example where we assume that detected signals corresponding to $\rho > 0.9$ cannot be safely distinguished due to technical restrictions of the detection system. For $\rho > 0.9$, $\rho_{\mathrm{eff}}=1$, so the detection system cannot distinguish the states of interest even by increasing the level of the signal. On the contrary, for smaller values of $\rho$, accessible making use of a weak amplification scheme, this limitation does not exist since the detection system can resolve this modes when enough signal is present.

![Effective mode overlap. For $\rho>0.9$ the detection system cannot distinguish the states of interest. Data: $a=0.9$ and $n=100$.[]{data-label="figure_effective_rho"}](figure5.eps){width="50.00000%"}

Advantages of using weak value amplification (III): enhancement of the Fisher information {#advantages-of-using-weak-value-amplification-iii-enhancement-of-the-fisher-information .unnumbered}
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Up to now, we have used the 