Advantages of nonclassical pointer states in postselected weak measurements

Abstract

We investigate, within the weak measurement theory, the advantages of nonclassical pointer states over semiclassical ones for coherent, squeezed vacuum, and Schrödinger cat states. These states are utilized as pointer states for the system operator  with property Â2=Î, where Î represents the identity operator. We calculate the ratio between the signal-to-noise ratio of nonpostselected and postselected weak measurements. The latter is used to find the quantum Fisher information for the above pointer states. The average shifts for those pointer states with arbitrary interaction strength are investigated in detail. One key result is that we find the postselected weak measurement scheme for nonclassical pointer states to be superior to semiclassical ones. This can improve the precision of the measurement process.