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arXiv · 2604.20303

Operational criterion for Wigner function negativity

Paolo Solinas·Beatrice Donelli·Stefano Gherardini
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Abstract

We introduce an operational criterion to identify Wigner function (WF) negativity for an arbitrary quantum state within the framework of quantum non-demolition measurements. This criterion corresponds to experimentally accessible schemes that enable a direct measurement of the WF, and establishes the coherent-state basis as a privileged basis for determining when the WF exhibits negative regions. We show that the absence (presence) of coherent superpositions in the coherent-state basis provides direct information about the positivity (negativity) of the WF. In particular, the absence of such superpositions constitutes a sufficient condition for WF positivity. Although a general proof of necessity remains elusive, we demonstrate that this condition is also necessary in two relevant cases: Schr\"{o}dinger-cat states and higher-order cat states on a circle. More precisely, for Schr\"{o}dinger-cat states we establish a necessary and sufficient condition for the positivity of the WF in full generality, whereas for high-order cat states on a circle we derive an analogous condition in the limit of a large number of densely packed coherent states.

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Paolo Solinas, Beatrice Donelli, Stefano Gherardini. 2026-04-22. Operational criterion for Wigner function negativity. https://arxiv.org/abs/2604.20303

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