Paolo Solinas - Università di Genova and INFN

Operational criterion for Wigner function negativity

In this talk, I will present an operational criterion to identify negativity of the Wigner function (WF) for arbitrary quantum states within the framework of quantum non-demolition measurements. This approach highlights the coherent-state basis as a natural setting to assess the presence of negative regions.

I will show how the absence or presence of coherent superpositions in this basis provides direct information about WF positivity or negativity. In particular, I will discuss a sufficient condition for WF positivity based on the absence of such superpositions, and examine the extent to which this condition is also necessary.

Finally, I will illustrate these results in relevant examples, including Schrödinger-cat states—where a necessary and sufficient condition can be established—and high-order cat states on a circle, for which an analogous condition emerges in the large-number limit.