Design of an optimal quantum receiver for interferometric sensing devices

A practically realizable detection scheme that corresponds to the optimal measurement strategy within the Neyman-Pearson approach is proposed. The pure state probe field is generally described by | ψ₀> = Uˆ|0>, where Uˆ is the unitary operator that defines the quantum property of the probe field. The prepared probe field is incident into the black box in which the unitary perturbative operation Uˆ_p(g) sometimes occurs, where g is the small parameter, such as the small phase shift, to be detected. The output field (|ψ₀> or |ψ₁> = Uˆ_p(g) |ψ₀> ) is then measured by the positive operator-valued measure (POVM) which consists of the reverse process of the preparation of the probe field and the photodetection process that discriminates if the field includes zero or non-zero photons. This is an application of the Kennedy detection scheme which has been considered as the detector for a binary communications system. The detection probability of the scheme is given by P_d = 1-|<ψ₀|Uˆ_p(g) |ψ₀>|² that is what expected from the mathematical optimization procedure of the Neyman-Pearson hypothesis testing. The scheme is easily applicable to various quantum states such as the coherent or the squeezed probe fields, and so on.