Single- and two-mode quantumness at a beam splitter

TL;DR

This paper investigates the relationship between two notions of classicality in bipartite bosonic systems, revealing that P-classicality and C-classicality are largely incompatible and exploring how P-classicality influences entanglement generation at a beam splitter.

Contribution

It provides a quantitative analysis of the dynamical relation between P- and C-classicality in a quantum-optical setting, linking non-classical depth to entanglement potential.

Findings

Almost all P-classical states produce non-C-classical outputs.

More P-classical resources lead to less C-classicality at the output.

Non-classical depth determines the maximum thermal photons for entanglement preservation.

Abstract

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.