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√n̄)^-1 versus the average photon number n̄, while it can be improved to (2n̄)^-1 by using displaced squeezed states.
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Chiribella et al. (2006) studied this question.
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