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 (2 root n)(-1) versus the average photon number (n) over bar, while it can be improved to (2 (n) over bar)(-1) by using displaced squeezed states.