Wigner function negativity in a classical model of quantum light
Brian R. La Cour
TL;DR
This work investigates whether Wigner-function negativity, often taken as a signature of nonclassicality, can arise from a classical model when combined with tomographic post-selection. The authors build a classical light model with real vacuum modes, Bogoliubov-type transformations to simulate squeezing, and threshold-based heralding, then perform tomographic inference to obtain the density matrix $\rho_{nm}$ and the Wigner function $W(\alpha)=\sum_{n,m} \rho_{nm}W_{nm}(\alpha)$. Numerical simulations show negativity in the inferred Wigner functions for both vacuum- and SPACS-like states, with minima $-0.11$ and $-0.29$ respectively, and high fidelity to experimental observations though with higher-order-mode deviations. The results emphasize that Wigner negativity can emerge from classical post-selection and inference, underscoring the need to carefully interpret negativity in SPACS-type experiments and the role of heralding schemes and mode structure in such analyses.
Abstract
The presence of negative values in the Wigner quasiprobability distribution is deemed one of the hallmarks of nonclassical phenomena in quantum systems. Here we demonstrate a classical model of squeezed light that, when combined with post-selection on amplitude threshold-crossing detection events, is capable of reproducing observed behavior of single-photon added coherent states. In particular, a classical model of balanced homodyne detection and standard tomographic techniques are used to infer the density matrix in the Fock basis. The resulting Wigner functions exhibit negatively for photon-added vacuum and weak coherent states.