Higher-order nonclassicality criteria for photon-subtracted and photon-added states via the normalization constant

TL;DR

The paper introduces a unified, efficient method to evaluate higher-order nonclassicality criteria for photon-subtracted and photon-added states by reordering factorial moments to depend solely on the state's normalization constant. It derives explicit, order-dependent expressions for key criteria—the generalized Mandel $Q^{(\ell)}$, Lee antibunching $d^{(\ell-1)}_h$, and Agarwal–Tara $A_3$—and demonstrates how to compute them from normalization constants for both subtraction and addition scenarios. For photon-subtracted states, factorial moments naturally reduce to simple ratios of normalization constants, yielding compact formulas such as $Q = N_{m+2}/N_{m+1} - N_{m+1}/N_m$ and $d_h^{(x-1)} = N_{n+x}/N_n - (N_{n+1}/N_n)^x$; for photon-added states, a general identity for $a^{\dagger x} a^x$ leads to a similarly explicit expression in terms of $N_n$, with the Mandel parameter matching previous IWOP results. Overall, the approach streamlines the assessment of higher-order nonclassicality, enabling straightforward characterization of nonclassical states in terms of a single normalization constant.

Abstract

We show that any nonclassicality criterion based on factorial moments, including several higher-order parameters such as the Mandel $Q^{(\ell)}$ parameter, the Lee antibunching function $d^{(\ell-1)}_h$, and the Agarwal--Tara parameter $A_3$, can be computed straightforwardly for photon-subtracted and photon-added states by performing operator reordering of the factorial moments. Within this approach, all relevant quantities depend solely on the normalization constant of the given state.