Nonquantum information gain from higher-order correlation functions

Abstract

Nonlinear correlation functions are at the heart of quantum theory. The second-order correlation function g^{(2)}(τ) has been a cornerstone of quantum optics for over half a century, and a myriad of quantum and classical applications has been discovered. In contrast, higher-order correlation functions have so far been used only to reveal the nonclassical character of the emitted fields. In this paper, we study the relation between the kth-order correlation function g^{(k)}(0) and the projection of the underlying quantum state of light onto the subspace of Fock states with a photon number less than k. We show that when g^{(k)}(0) falls below a critical value, lower bounds for the projection on this subspace can be concluded as well as on the ratio of the subspace with one to k−1 photons and k to infinity. These bounds are, at face value, valid for only nonclassical quantum states. However, when the quantum state includes a nonzero projection on the vacuum state, the value of g^{(k)}(0) is artificially enhanced, potentially covering these projections. We derive an effective kth-order correlation function, which accounts for the effect of vacuum. We show that the information gained from the effective correlation function is not limited to nonclassical quantum states and thus constitutes a quantum and classical application of higher-order correlation functions.