Single- and two-mode quantumness at a beam splitter

In the context of bipartite bosonic systems, two notions of classicality of correlations can be defined: P-classicality, based on the properties of the Glauber-Sudarshan P-function; and C-classicality, based on the entropic quantum discord. It has been shown that these two notions are maximally inequivalent in a static (metric) sense -- as they coincide only on a set of states of zero measure. We extend and reinforce quantitatively this inequivalence by addressing the dynamical relation between these types of non-classicality in a paradigmatic quantum-optical setting: the linear mixing at a beam splitter of a single-mode Gaussian state with a thermal reference state. Specifically, we show that almost all P-classical input states generate outputs that are not C-classical. Indeed, for the case of zero thermal reference photons, the more P-classical resources at the input the less C-classicality at the output. In addition, we show that the P-classicality at the input -- as quantified by the non-classical depth -- does instead determine quantitatively the potential of generating output entanglement. This endows the non-classical depth with a new operational interpretation: it gives the maximum number of thermal reference photons that can be mixed at a beam splitter without destroying the output entanglement.

Nonlinearity as a resource for nonclassicality in anharmonic systems

Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macro- scopic quantum coherence. Considering various exactly-solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the the entropic nonlinearity of the considered potentials and their ground state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing--which is not captured by the negativity of the Wigner function--we focus on the Glauber-Sudarshan P-function and address the nonclassicality/nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.