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> = Û|₀>, where Û 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 Û_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> = Û_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|Û_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.