Entanglement-enhanced phase estimation with Weyl-quantized self-Kerr generators

Abstract

We investigate entanglement-enhanced phase estimation using a Weyl-quantized self-Kerr generator in a nonlinear Mach−Zehnder interferometer. Motivated by nonlinear interferometric schemes in Kerr media, where the refractive index and accumulated phase depend on optical intensity, we model the unknown phase as being encoded by the Weyl-ordered generator H_W = κℏ²ω²(n̂² + n̂ + 1/2). The constant Weyl correction contributes only a removable global phase, while the quadratic and linear photon-number terms determine the relative phase acquired by an entangled N00N probe. For the input state |ψ〉=(|N,0〉+ |0,N〉)/√2, the resulting measurement signal depends on θκℏ²ω²(N²+N). Error propagation then gives the phase sensitivity Δθ ≥ [κℏ²ω²(N²+N)]⁻¹, which approaches a 1/N² scaling for large photon number. This result shows that, within the ideal lossless model considered here, the Weyl-quantized self-Kerr interaction can provide a nonlinear metrological enhancement beyond the usual entanglement-assisted linear-interferometric scaling.