Optimal encoding of phase information in trapped ions

We propose a specific preparation of a set of N two-level ions (i.e., the c ollective state <(Omega)over cap> of these ions) in which the information a bout the phase can be most optimally encoded. The phase psi in this context refers to a continuous parameter psi is an element of < 0, 2 pi > which la bels different points along the evolution path of a given state <(Omega)ove r cap> of the N-ion system described by a unitary one-parametric group U(ps i) = exp{-i psi (H) over cap}. The optimality of the preparation of the giv en quantum system means that using the optimal measurement scheme the phase psi encoded in the system of N two-level ions can be "extracted" (decoded) with the highest mean fidelity.