Equivalence of contextuality and Wigner function negativity in continuous-variable quantum optics

• URL: http://arxiv.org/abs/2112.14788v1
• Date: Wed, 29 Dec 2021 19:01:51 GMT
• Title: Equivalence of contextuality and Wigner function negativity in continuous-variable quantum optics
• Authors: Jonas Haferkamp, Juani Bermejo-Vega
• Abstract summary: In quantum optics, the non-negativity of the Wigner function is a ubiquitous notion of classicality. We show that any non-contextual hidden variable model for Gaussian quantum optics has an alternative non-negative Wigner function description.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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