Wigner function negativity in a classical model of quantum light

Brian R. La Cour

Brian R. La Cour

Brian R. La Cour

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.

Trevor W. Marshall, Emilio Santos

Jonas Haferkamp, Juan Bermejo-Vega

One of the central foundational questions of physics is to identify what makes a system quantum as opposed to classical. One seminal notion of classicality of a quantum system is the existence of a non-contextual hidden variable model as introduced in the early work by Bell, Kochen and Specker. In quantum optics, the non-negativity of the Wigner function is a ubiquitous notion of classicality. In this work we establish an equivalence between these two concepts. In particular, we show that any non-contextual hidden variable model for Gaussian quantum optics has an alternative non-negative Wigner function description. Conversely, it was known that the Wigner representation provides a non-negative non-contextual description of Gaussian quantum optics. It follows that contextuality and Wigner negativity are equivalent notions of non-classicality and equivalent resources for this quantum subtheory. In particular, both contextuality and Wigner negativity are necessary for a computational speed-up of quantum Gaussian optics. At the technical level, our result holds true for any subfamily of Gaussian measurements that include homodyne measurements, i.e., measurements of standard quadrature observables.

I. Földesi, József Janszky, Петер Адам +3 more