Weak value amplification for nonunitary evolution

We discuss interferometric parameter estimation of the amplitude, instead of the phase, via weak value amplification. The considered weak interaction introduces modulation on the amplitude of the wave function; therefore, the two-party state experiences a nonunitary evolution. With the same pre- and postselection states as those of original weak value amplification, a much larger anomalous amplification factor can be attained. The shift in the intensity profile at the dark port and the signal-to-noise ratio for the parameter of interest get further amplified by the weak value, compared to phase-based weak value amplification. Although the nonunitary evolution introduces loss, more information about the parameter of interest can be extracted. Thus the weak value amplification is extended to measurement of amplitude and nonunitary processes. We also discuss possible applications of this idea for precisely measuring tiny rotations or enhancing the image contrast of transparent objects.