Phase estimation using Kerr-type generators from Weyl and Born-Jordan quantized polynomials with coherent states

Abstract

Using nonlinear media such as Kerr-type media in quantum metrology can enhance interferometric measurements up to the super-Heisenberg limit. However, using nonlinear classical polynomials can cause operator ambiguities when quantized. This study investigates the effect of using different quantization schemes, specifically Weyl and Born-Jordan, on the phase sensitivity of a Kerr-type generator with classical polynomial p²q². By acting the generator on coherent states and calculating the quantum Fisher information (QFI), the resulting minimum phase sensitivity for both Weyl and Born-Jordan quantized Hamiltonians remains identical, as both generators only differ by a constant.