Metrological Nonlinear Squeezing Parameter

The well-known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results lead to optimized and experimentally feasible recipes for a high-precision moment-based estimation of a phase parameter and can be used to systematically construct multipartite entanglement and nonclassicality witnesses for complex quantum states.

Figure 1

Analytically optimized nonlinear spin squeezing coefficients ${\xi }_{(K)}^{-2}$ for $K=2,\dots ,5$ compared to the linear spin squeezing coefficient ${\xi }_{(1)}^{-2}$, the spin parity squeezing coefficient ${\xi }_P^{-2}$, and the quantum Fisher density $f_{\max }$ for the states $|{\mathrm{\Psi }}_{\mathrm{OAT}}(\tau )⟩$ [$N=16$ in (a) and $N=100$ in (b)], as well as the Wigner function of selected states with $N=100$ (c). Panels (d),(e), and (f) show the same data for the states $|{\mathrm{\Psi }}_{\mathrm{TAT}}(\tau )⟩$.