  In quantum metrology, it is widely believed that the quantum Cramer-Rao bound
is attainable bound while it is not true. In order to clarify this point, we
explain why the quantum Cramer-Rao bound cannot be attained geometrically. In
this manuscript, we investigate noiseless channel estimation under energy
constraint for states, using a physically reasonable error function, and
present the optimal state and the attainable bound. We propose the experimental
generation of the optimal states for enhanced metrology using squeezing
transformations. This makes the estimation of unitary channels physically
implementable, while existing unitary estimation protocols do not work
