  To describe the pre- and post-selected quantum ensembles, a complex quantity
called the weak value of an operator is used. The weak value is highly
controversial due to the fact that it is not bounded by the possible
eigenvalues of the corresponding operator. Nevertheless, the obtaining of the
anomalous weak value is regarded as a powerful technique in the quantum
interferometry nowadays. Here it is shown that the postselection on a quantum
system recovers a completely hidden interference effect in the measurement
apparatus. Studying the interference pattern shows the optimal settings for the
amplification and the parameter estimation. It also proves that the weak value
is not an element of reality. Using single photons, it is investigated how a
postselected photon can impart a $\pi$ phase shift (the peak of the
amplification) to a photon interacting weakly with it in a nonlinear optical
medium. The increasing of the degree of the entanglement lies behind the
effectiveness of the postselection in the parameter estimation. In particular,
arranging to postselect on pure entangled states can optimize the
signal-to-noise ratio, allowing to achieve high-sensitive measurements using
low input power.

Quantum Physics