In this work we generalize the Bochner criterion addressing the characteristic function, i.e., the Fourier transform, of the Glauber-Sudarshan phase-space function. For this purpose we extend the Bochner theorem by including derivatives of the characteristic function. The resulting necessary and sufficient nonclassicality criteria unify previously known moment-based criteria with those based on the characteristic function. For applications of the generalized nonclassicality probes, we provide direct sampling formulas for balanced homodyne detection. A squeezed vacuum state is experimentally realized and characterized with our method. This complete framework—theoretical unification, sampling approach, and experimental implementation—presents an efficient toolbox to characterize quantum states of light for applications in quantum technology.

• Received 22 May 2015

DOI:https://doi.org/10.1103/PhysRevA.92.011801