Optimal estimation of squeezing

We present the optimal estimation of an unknown squeezing transformation of the radiation field. The optimal estimation is unbiased and is obtained by properly considering the degeneracy of the squeezing operator. For coherent input states, the root-mean square of the estimation scales as ${\left(2\sqrt{\overline{n}}\right)}^{-1}$ versus the average photon number $\overline{n}$, while it can be improved to ${\left(2\overline{n}\right)}^{-1}$ by using displaced squeezed states.

Figure 1

Probability distributions for the estimation of squeezing on a vacuum input state. The asymmetric distribution comes from the suboptimal measurement of Ref. 7 in Eq. (16). The symmetric distribution corresponds to the optimal measurement of Eq. (12).

Figure 2

Optimal probability distribution of squeezing for input coherent states. The distribution becomes sharper for increasing values of the coherent-state amplitude $(\alpha =1,2,4)$.